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        <p style="Chapter Head" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">WAVELETS EXTENSION PACK</p>
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        <p style="Section Title" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Appendix C: Additional Wavelet Functions</p>
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">The MaxDWTLevel function returns the largest level allowable for the DWT of a particular array or matrix.</p>
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        <p style="Heading 1" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Functions for rescaling two-dimensional (2D) wavelet packet transforms for viewing with the picture operator.</p>
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        <phrase>multiresolution analysis functions</phrase>
      </indexes>
    </region>
    <region region-id="4910" left="6" top="633" width="359.25" height="138" align-x="69.75" align-y="642" show-border="false" show-highlight="false" is-protected="true" background-color="#ff8000" tag="">
      <math optimize="false" export="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id>mra</ml:id>
            <ml:boundVars>
              <ml:id>v</ml:id>
              <ml:id>J</ml:id>
              <ml:id>filter</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:program>
            <ml:localDefine>
              <ml:id>w</ml:id>
              <ml:apply>
                <ml:id>dwt</ml:id>
                <ml:sequence>
                  <ml:id>v</ml:id>
                  <ml:id>J</ml:id>
                  <ml:id>filter</ml:id>
                </ml:sequence>
              </ml:apply>
            </ml:localDefine>
            <ml:localDefine>
              <ml:apply>
                <ml:indexer />
                <ml:id>Z</ml:id>
                <ml:apply>
                  <ml:minus />
                  <ml:apply>
                    <ml:id>rows</ml:id>
                    <ml:id>v</ml:id>
                  </ml:apply>
                  <ml:real>1</ml:real>
                </ml:apply>
              </ml:apply>
              <ml:real>0</ml:real>
            </ml:localDefine>
            <ml:localDefine>
              <ml:apply>
                <ml:matcol />
                <ml:id>M</ml:id>
                <ml:real>0</ml:real>
              </ml:apply>
              <ml:apply>
                <ml:id>idwt</ml:id>
                <ml:sequence>
                  <ml:apply>
                    <ml:id>put_smooth</ml:id>
                    <ml:sequence>
                      <ml:id>Z</ml:id>
                      <ml:id>J</ml:id>
                      <ml:apply>
                        <ml:id>get_smooth</ml:id>
                        <ml:sequence>
                          <ml:id>w</ml:id>
                          <ml:id>J</ml:id>
                        </ml:sequence>
                      </ml:apply>
                    </ml:sequence>
                  </ml:apply>
                  <ml:id>J</ml:id>
                  <ml:id>filter</ml:id>
                </ml:sequence>
              </ml:apply>
            </ml:localDefine>
            <ml:for>
              <ml:id>qj</ml:id>
              <ml:range>
                <ml:id>J</ml:id>
                <ml:real>1</ml:real>
              </ml:range>
              <ml:program>
                <ml:localDefine>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>Z</ml:id>
                    <ml:apply>
                      <ml:minus />
                      <ml:apply>
                        <ml:id>rows</ml:id>
                        <ml:id>v</ml:id>
                      </ml:apply>
                      <ml:real>1</ml:real>
                    </ml:apply>
                  </ml:apply>
                  <ml:real>0</ml:real>
                </ml:localDefine>
                <ml:localDefine>
                  <ml:apply>
                    <ml:matcol />
                    <ml:id>M</ml:id>
                    <ml:apply>
                      <ml:minus />
                      <ml:apply>
                        <ml:plus />
                        <ml:id>J</ml:id>
                        <ml:real>1</ml:real>
                      </ml:apply>
                      <ml:id>qj</ml:id>
                    </ml:apply>
                  </ml:apply>
                  <ml:apply>
                    <ml:id>idwt</ml:id>
                    <ml:sequence>
                      <ml:apply>
                        <ml:id>put_detail</ml:id>
                        <ml:sequence>
                          <ml:id>Z</ml:id>
                          <ml:id>qj</ml:id>
                          <ml:apply>
                            <ml:id>get_detail</ml:id>
                            <ml:sequence>
                              <ml:id>w</ml:id>
                              <ml:id>qj</ml:id>
                            </ml:sequence>
                          </ml:apply>
                        </ml:sequence>
                      </ml:apply>
                      <ml:id>J</ml:id>
                      <ml:id>filter</ml:id>
                    </ml:sequence>
                  </ml:apply>
                </ml:localDefine>
              </ml:program>
            </ml:for>
            <ml:apply>
              <ml:transpose />
              <ml:id>M</ml:id>
            </ml:apply>
          </ml:program>
        </ml:define>
      </math>
      <indexes>
        <phrase>mra function</phrase>
      </indexes>
      <rendering item-idref="10" />
    </region>
    <region region-id="4911" left="6" top="795" width="222.75" height="105.75" align-x="92.25" align-y="804" show-border="false" show-highlight="false" is-protected="true" background-color="#ff8000" tag="">
      <math optimize="false" export="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id>mrapprox</ml:id>
            <ml:boundVars>
              <ml:id>y</ml:id>
              <ml:id>J</ml:id>
              <ml:id>filter</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:program>
            <ml:localDefine>
              <ml:id>Q</ml:id>
              <ml:apply>
                <ml:id>mra</ml:id>
                <ml:sequence>
                  <ml:id>y</ml:id>
                  <ml:id>J</ml:id>
                  <ml:id>filter</ml:id>
                </ml:sequence>
              </ml:apply>
            </ml:localDefine>
            <ml:for>
              <ml:id>i</ml:id>
              <ml:range>
                <ml:real>0</ml:real>
                <ml:apply>
                  <ml:minus />
                  <ml:apply>
                    <ml:id>rows</ml:id>
                    <ml:id>y</ml:id>
                  </ml:apply>
                  <ml:real>1</ml:real>
                </ml:apply>
              </ml:range>
              <ml:program>
                <ml:localDefine>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>M</ml:id>
                    <ml:sequence>
                      <ml:real>0</ml:real>
                      <ml:id>i</ml:id>
                    </ml:sequence>
                  </ml:apply>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>Q</ml:id>
                    <ml:sequence>
                      <ml:real>0</ml:real>
                      <ml:id>i</ml:id>
                    </ml:sequence>
                  </ml:apply>
                </ml:localDefine>
                <ml:for>
                  <ml:id>j</ml:id>
                  <ml:range>
                    <ml:real>1</ml:real>
                    <ml:id>J</ml:id>
                  </ml:range>
                  <ml:localDefine>
                    <ml:apply>
                      <ml:indexer />
                      <ml:id>M</ml:id>
                      <ml:sequence>
                        <ml:id>j</ml:id>
                        <ml:id>i</ml:id>
                      </ml:sequence>
                    </ml:apply>
                    <ml:apply>
                      <ml:plus />
                      <ml:apply>
                        <ml:indexer />
                        <ml:id>M</ml:id>
                        <ml:sequence>
                          <ml:apply>
                            <ml:minus />
                            <ml:id>j</ml:id>
                            <ml:real>1</ml:real>
                          </ml:apply>
                          <ml:id>i</ml:id>
                        </ml:sequence>
                      </ml:apply>
                      <ml:apply>
                        <ml:indexer />
                        <ml:id>Q</ml:id>
                        <ml:sequence>
                          <ml:id>j</ml:id>
                          <ml:id>i</ml:id>
                        </ml:sequence>
                      </ml:apply>
                    </ml:apply>
                  </ml:localDefine>
                </ml:for>
              </ml:program>
            </ml:for>
            <ml:id>M</ml:id>
          </ml:program>
        </ml:define>
      </math>
      <indexes>
        <phrase>mrapprox function</phrase>
      </indexes>
      <rendering item-idref="11" />
    </region>
    <region region-id="4445" left="6" top="912.75" width="169.5" height="14.25" align-x="6" align-y="924" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Heading 1" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Wavelet Approximation Functions</p>
      </text>
      <indexes>
        <phrase>wavelet approximation functions</phrase>
      </indexes>
    </region>
    <region region-id="4912" left="6" top="933" width="228" height="128.25" align-x="112.5" align-y="942" show-border="false" show-highlight="false" is-protected="true" background-color="#ffff80" tag="">
      <math optimize="false" export="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id>waveapprox</ml:id>
            <ml:boundVars>
              <ml:id>x</ml:id>
              <ml:id>J</ml:id>
              <ml:id>n</ml:id>
              <ml:id>filter</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:program>
            <ml:localDefine>
              <ml:id>w</ml:id>
              <ml:apply>
                <ml:id>dwt</ml:id>
                <ml:sequence>
                  <ml:id>x</ml:id>
                  <ml:id>J</ml:id>
                  <ml:id>filter</ml:id>
                </ml:sequence>
              </ml:apply>
            </ml:localDefine>
            <ml:localDefine>
              <ml:id>ws</ml:id>
              <ml:apply>
                <ml:id>reverse</ml:id>
                <ml:apply>
                  <ml:id>sort</ml:id>
                  <ml:apply>
                    <ml:vectorize />
                    <ml:apply>
                      <ml:absval />
                      <ml:id>w</ml:id>
                    </ml:apply>
                  </ml:apply>
                </ml:apply>
              </ml:apply>
            </ml:localDefine>
            <ml:localDefine>
              <ml:id subscript="w">T</ml:id>
              <ml:apply>
                <ml:indexer />
                <ml:id>ws</ml:id>
                <ml:apply>
                  <ml:minus />
                  <ml:id>n</ml:id>
                  <ml:real>1</ml:real>
                </ml:apply>
              </ml:apply>
            </ml:localDefine>
            <ml:for>
              <ml:id>i</ml:id>
              <ml:range>
                <ml:real>0</ml:real>
                <ml:apply>
                  <ml:minus />
                  <ml:apply>
                    <ml:id>rows</ml:id>
                    <ml:id>w</ml:id>
                  </ml:apply>
                  <ml:real>1</ml:real>
                </ml:apply>
              </ml:range>
              <ml:localDefine>
                <ml:apply>
                  <ml:indexer />
                  <ml:id>wt</ml:id>
                  <ml:id>i</ml:id>
                </ml:apply>
                <ml:apply>
                  <ml:mult style="default" />
                  <ml:parens>
                    <ml:apply>
                      <ml:greaterOrEqual />
                      <ml:apply>
                        <ml:absval />
                        <ml:apply>
                          <ml:indexer />
                          <ml:id>w</ml:id>
                          <ml:id>i</ml:id>
                        </ml:apply>
                      </ml:apply>
                      <ml:id subscript="w">T</ml:id>
                    </ml:apply>
                  </ml:parens>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>w</ml:id>
                    <ml:id>i</ml:id>
                  </ml:apply>
                </ml:apply>
              </ml:localDefine>
            </ml:for>
            <ml:localDefine>
              <ml:id>R</ml:id>
              <ml:apply>
                <ml:id>idwt</ml:id>
                <ml:sequence>
                  <ml:id>wt</ml:id>
                  <ml:id>J</ml:id>
                  <ml:id>filter</ml:id>
                </ml:sequence>
              </ml:apply>
            </ml:localDefine>
            <ml:id>R</ml:id>
          </ml:program>
        </ml:define>
      </math>
      <indexes>
        <phrase>waveapprox function</phrase>
      </indexes>
      <rendering item-idref="12" />
    </region>
    <region region-id="4913" left="6" top="1095" width="251.25" height="196.5" align-x="117" align-y="1104" show-border="false" show-highlight="false" is-protected="true" background-color="#ffff80" tag="">
      <math optimize="false" export="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id>wavedecomp</ml:id>
            <ml:boundVars>
              <ml:id>x</ml:id>
              <ml:id>J</ml:id>
              <ml:id>n</ml:id>
              <ml:id>filter</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:program>
            <ml:localDefine>
              <ml:id>w</ml:id>
              <ml:apply>
                <ml:id>dwt</ml:id>
                <ml:sequence>
                  <ml:id>x</ml:id>
                  <ml:id>J</ml:id>
                  <ml:id>filter</ml:id>
                </ml:sequence>
              </ml:apply>
            </ml:localDefine>
            <ml:for>
              <ml:id>i</ml:id>
              <ml:range>
                <ml:real>0</ml:real>
                <ml:apply>
                  <ml:minus />
                  <ml:apply>
                    <ml:id>rows</ml:id>
                    <ml:id>w</ml:id>
                  </ml:apply>
                  <ml:real>1</ml:real>
                </ml:apply>
              </ml:range>
              <ml:localDefine>
                <ml:apply>
                  <ml:indexer />
                  <ml:id>w</ml:id>
                  <ml:sequence>
                    <ml:id>i</ml:id>
                    <ml:real>1</ml:real>
                  </ml:sequence>
                </ml:apply>
                <ml:id>i</ml:id>
              </ml:localDefine>
            </ml:for>
            <ml:localDefine>
              <ml:id>ws</ml:id>
              <ml:apply>
                <ml:id>reverse</ml:id>
                <ml:apply>
                  <ml:id>csort</ml:id>
                  <ml:sequence>
                    <ml:apply>
                      <ml:vectorize />
                      <ml:apply>
                        <ml:absval />
                        <ml:id>w</ml:id>
                      </ml:apply>
                    </ml:apply>
                    <ml:real>0</ml:real>
                  </ml:sequence>
                </ml:apply>
              </ml:apply>
            </ml:localDefine>
            <ml:localDefine>
              <ml:apply>
                <ml:indexer />
                <ml:id>wt</ml:id>
                <ml:apply>
                  <ml:minus />
                  <ml:apply>
                    <ml:id>rows</ml:id>
                    <ml:id>w</ml:id>
                  </ml:apply>
                  <ml:real>1</ml:real>
                </ml:apply>
              </ml:apply>
              <ml:real>0</ml:real>
            </ml:localDefine>
            <ml:for>
              <ml:id>qq</ml:id>
              <ml:range>
                <ml:real>0</ml:real>
                <ml:apply>
                  <ml:minus />
                  <ml:id>n</ml:id>
                  <ml:real>1</ml:real>
                </ml:apply>
              </ml:range>
              <ml:program>
                <ml:localDefine>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>wt</ml:id>
                    <ml:apply>
                      <ml:indexer />
                      <ml:id>ws</ml:id>
                      <ml:sequence>
                        <ml:id>qq</ml:id>
                        <ml:real>1</ml:real>
                      </ml:sequence>
                    </ml:apply>
                  </ml:apply>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>w</ml:id>
                    <ml:sequence>
                      <ml:parens>
                        <ml:apply>
                          <ml:indexer />
                          <ml:id>ws</ml:id>
                          <ml:sequence>
                            <ml:id>qq</ml:id>
                            <ml:real>1</ml:real>
                          </ml:sequence>
                        </ml:apply>
                      </ml:parens>
                      <ml:real>0</ml:real>
                    </ml:sequence>
                  </ml:apply>
                </ml:localDefine>
                <ml:localDefine>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>R</ml:id>
                    <ml:id>qq</ml:id>
                  </ml:apply>
                  <ml:apply>
                    <ml:id>idwt</ml:id>
                    <ml:sequence>
                      <ml:id>wt</ml:id>
                      <ml:id>J</ml:id>
                      <ml:id>filter</ml:id>
                    </ml:sequence>
                  </ml:apply>
                </ml:localDefine>
                <ml:localDefine>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>wt</ml:id>
                    <ml:apply>
                      <ml:indexer />
                      <ml:id>ws</ml:id>
                      <ml:sequence>
                        <ml:id>qq</ml:id>
                        <ml:real>1</ml:real>
                      </ml:sequence>
                    </ml:apply>
                  </ml:apply>
                  <ml:real>0</ml:real>
                </ml:localDefine>
              </ml:program>
            </ml:for>
            <ml:id>R</ml:id>
          </ml:program>
        </ml:define>
      </math>
      <indexes>
        <phrase>wavedecomp function</phrase>
      </indexes>
      <rendering item-idref="13" />
    </region>
    <region region-id="4611" left="0" top="1308" width="6000" height="6" align-x="0" align-y="1308" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="">
      <pageBreak />
    </region>
    <region region-id="4449" left="6" top="1314.75" width="117.75" height="14.25" align-x="6" align-y="1326" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Heading 1" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Basis Selection Display</p>
      </text>
      <indexes>
        <phrase>basis selection display</phrase>
      </indexes>
    </region>
    <region region-id="4905" left="6" top="1338.75" width="332.25" height="42.75" align-x="6" align-y="1350" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">
          <f family="Times New Roman" charset="0" size="12">
            <inlineAttr line-through="false">For any selection of basis to be valid, it is necessary and sufficient that every column in the pgrid plot (see below) be covered, but also that there is no overlap in any column.</inlineAttr>
          </f>
        </p>
      </text>
    </region>
    <region region-id="4960" left="6" top="1395" width="306.75" height="476.25" align-x="89.25" align-y="1404" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="">
      <math optimize="false" export="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id>pgridplot</ml:id>
            <ml:boundVars>
              <ml:id>b</ml:id>
              <ml:id>levels</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:program>
            <ml:localDefine>
              <ml:id>levels</ml:id>
              <ml:apply>
                <ml:plus />
                <ml:id>levels</ml:id>
                <ml:real>1</ml:real>
              </ml:apply>
            </ml:localDefine>
            <ml:localDefine>
              <ml:id>cols</ml:id>
              <ml:apply>
                <ml:pow />
                <ml:real>2</ml:real>
                <ml:id>levels</ml:id>
              </ml:apply>
            </ml:localDefine>
            <ml:localDefine>
              <ml:id>hsize</ml:id>
              <ml:real>4</ml:real>
            </ml:localDefine>
            <ml:localDefine>
              <ml:id>vsize</ml:id>
              <ml:real>16</ml:real>
            </ml:localDefine>
            <ml:for>
              <ml:id>i</ml:id>
              <ml:range>
                <ml:real>0</ml:real>
                <ml:apply>
                  <ml:mult style="default" />
                  <ml:id>levels</ml:id>
                  <ml:id>vsize</ml:id>
                </ml:apply>
              </ml:range>
              <ml:for>
                <ml:id>j</ml:id>
                <ml:range>
                  <ml:real>0</ml:real>
                  <ml:apply>
                    <ml:mult style="default" />
                    <ml:id>cols</ml:id>
                    <ml:id>hsize</ml:id>
                  </ml:apply>
                </ml:range>
                <ml:localDefine>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>Q</ml:id>
                    <ml:sequence>
                      <ml:id>i</ml:id>
                      <ml:id>j</ml:id>
                    </ml:sequence>
                  </ml:apply>
                  <ml:real>220</ml:real>
                </ml:localDefine>
              </ml:for>
            </ml:for>
            <ml:for>
              <ml:id>i</ml:id>
              <ml:range>
                <ml:real>0</ml:real>
                <ml:apply>
                  <ml:minus />
                  <ml:apply>
                    <ml:id>rows</ml:id>
                    <ml:id>b</ml:id>
                  </ml:apply>
                  <ml:real>1</ml:real>
                </ml:apply>
              </ml:range>
              <ml:for>
                <ml:id>j</ml:id>
                <ml:range>
                  <ml:apply>
                    <ml:mult style="default" />
                    <ml:id>vsize</ml:id>
                    <ml:apply>
                      <ml:indexer />
                      <ml:id>b</ml:id>
                      <ml:sequence>
                        <ml:id>i</ml:id>
                        <ml:real>0</ml:real>
                      </ml:sequence>
                    </ml:apply>
                  </ml:apply>
                  <ml:apply>
                    <ml:mult style="default" />
                    <ml:id>vsize</ml:id>
                    <ml:parens>
                      <ml:apply>
                        <ml:plus />
                        <ml:apply>
                          <ml:indexer />
                          <ml:id>b</ml:id>
                          <ml:sequence>
                            <ml:id>i</ml:id>
                            <ml:real>0</ml:real>
                          </ml:sequence>
                        </ml:apply>
                        <ml:real>1</ml:real>
                      </ml:apply>
                    </ml:parens>
                  </ml:apply>
                </ml:range>
                <ml:program>
                  <ml:localDefine>
                    <ml:id>offset</ml:id>
                    <ml:apply>
                      <ml:mult style="default" />
                      <ml:apply>
                        <ml:pow />
                        <ml:real>2</ml:real>
                        <ml:apply>
                          <ml:minus />
                          <ml:id>levels</ml:id>
                          <ml:apply>
                            <ml:indexer />
                            <ml:id>b</ml:id>
                            <ml:sequence>
                              <ml:id>i</ml:id>
                              <ml:real>0</ml:real>
                            </ml:sequence>
                          </ml:apply>
                        </ml:apply>
                      </ml:apply>
                      <ml:id>hsize</ml:id>
                    </ml:apply>
                  </ml:localDefine>
                  <ml:for>
                    <ml:id>k</ml:id>
                    <ml:range>
                      <ml:apply>
                        <ml:mult style="default" />
                        <ml:id>offset</ml:id>
                        <ml:apply>
                          <ml:indexer />
                          <ml:id>b</ml:id>
                          <ml:sequence>
                            <ml:id>i</ml:id>
                            <ml:real>1</ml:real>
                          </ml:sequence>
                        </ml:apply>
                      </ml:apply>
                      <ml:apply>
                        <ml:mult style="default" />
                        <ml:id>offset</ml:id>
                        <ml:parens>
                          <ml:apply>
                            <ml:plus />
                            <ml:apply>
                              <ml:indexer />
                              <ml:id>b</ml:id>
                              <ml:sequence>
                                <ml:id>i</ml:id>
                                <ml:real>1</ml:real>
                              </ml:sequence>
                            </ml:apply>
                            <ml:real>1</ml:real>
                          </ml:apply>
                        </ml:parens>
                      </ml:apply>
                    </ml:range>
                    <ml:localDefine>
                      <ml:apply>
                        <ml:indexer />
                        <ml:id>Q</ml:id>
                        <ml:sequence>
                          <ml:id>j</ml:id>
                          <ml:id>k</ml:id>
                        </ml:sequence>
                      </ml:apply>
                      <ml:real>127</ml:real>
                    </ml:localDefine>
                  </ml:for>
                </ml:program>
              </ml:for>
            </ml:for>
            <ml:for>
              <ml:id>i</ml:id>
              <ml:range>
                <ml:real>0</ml:real>
                <ml:apply>
                  <ml:minus />
                  <ml:id>levels</ml:id>
                  <ml:real>1</ml:real>
                </ml:apply>
              </ml:range>
              <ml:program>
                <ml:localDefine>
                  <ml:id>divisions</ml:id>
                  <ml:apply>
                    <ml:pow />
                    <ml:real>2</ml:real>
                    <ml:id>i</ml:id>
                  </ml:apply>
                </ml:localDefine>
                <ml:localDefine>
                  <ml:id>offset</ml:id>
                  <ml:apply>
                    <ml:pow />
                    <ml:real>2</ml:real>
                    <ml:apply>
                      <ml:minus />
                      <ml:id>levels</ml:id>
                      <ml:id>i</ml:id>
                    </ml:apply>
                  </ml:apply>
                </ml:localDefine>
                <ml:for>
                  <ml:id>j</ml:id>
                  <ml:range>
                    <ml:real>0</ml:real>
                    <ml:apply>
                      <ml:minus />
                      <ml:id>divisions</ml:id>
                      <ml:real>1</ml:real>
                    </ml:apply>
                  </ml:range>
                  <ml:for>
                    <ml:id>k</ml:id>
                    <ml:range>
                      <ml:sequence>
                        <ml:apply>
                          <ml:mult style="default" />
                          <ml:id>i</ml:id>
                          <ml:id>vsize</ml:id>
                        </ml:apply>
                        <ml:parens>
                          <ml:apply>
                            <ml:plus />
                            <ml:apply>
                              <ml:mult style="default" />
                              <ml:id>i</ml:id>
                              <ml:id>vsize</ml:id>
                            </ml:apply>
                            <ml:real>2</ml:real>
                          </ml:apply>
                        </ml:parens>
                      </ml:sequence>
                      <ml:apply>
                        <ml:mult style="default" />
                        <ml:parens>
                          <ml:apply>
                            <ml:plus />
                            <ml:id>i</ml:id>
                            <ml:real>1</ml:real>
                          </ml:apply>
                        </ml:parens>
                        <ml:id>vsize</ml:id>
                      </ml:apply>
                    </ml:range>
                    <ml:localDefine>
                      <ml:apply>
                        <ml:indexer />
                        <ml:id>Q</ml:id>
                        <ml:sequence>
                          <ml:id>k</ml:id>
                          <ml:apply>
                            <ml:mult style="default" />
                            <ml:apply>
                              <ml:mult style="default" />
                              <ml:id>offset</ml:id>
                              <ml:id>j</ml:id>
                            </ml:apply>
                            <ml:id>hsize</ml:id>
                          </ml:apply>
                        </ml:sequence>
                      </ml:apply>
                      <ml:real>0</ml:real>
                    </ml:localDefine>
                  </ml:for>
                </ml:for>
                <ml:for>
                  <ml:id>j</ml:id>
                  <ml:range>
                    <ml:sequence>
                      <ml:real>0</ml:real>
                      <ml:real>2</ml:real>
                    </ml:sequence>
                    <ml:apply>
                      <ml:mult style="default" />
                      <ml:id>cols</ml:id>
                      <ml:id>hsize</ml:id>
                    </ml:apply>
                  </ml:range>
                  <ml:localDefine>
                    <ml:apply>
                      <ml:indexer />
                      <ml:id>Q</ml:id>
                      <ml:sequence>
                        <ml:apply>
                          <ml:mult style="default" />
                          <ml:id>i</ml:id>
                          <ml:id>vsize</ml:id>
                        </ml:apply>
                        <ml:id>j</ml:id>
                      </ml:sequence>
                    </ml:apply>
                    <ml:real>0</ml:real>
                  </ml:localDefine>
                </ml:for>
              </ml:program>
            </ml:for>
            <ml:for>
              <ml:id>i</ml:id>
              <ml:range>
                <ml:sequence>
                  <ml:real>0</ml:real>
                  <ml:real>2</ml:real>
                </ml:sequence>
                <ml:apply>
                  <ml:mult style="default" />
                  <ml:id>levels</ml:id>
                  <ml:id>vsize</ml:id>
                </ml:apply>
              </ml:range>
              <ml:localDefine>
                <ml:apply>
                  <ml:indexer />
                  <ml:id>Q</ml:id>
                  <ml:sequence>
                    <ml:id>i</ml:id>
                    <ml:apply>
                      <ml:mult style="default" />
                      <ml:id>cols</ml:id>
                      <ml:id>hsize</ml:id>
                    </ml:apply>
                  </ml:sequence>
                </ml:apply>
                <ml:real>0</ml:real>
              </ml:localDefine>
            </ml:for>
            <ml:for>
              <ml:id>j</ml:id>
              <ml:range>
                <ml:sequence>
                  <ml:real>0</ml:real>
                  <ml:real>2</ml:real>
                </ml:sequence>
                <ml:apply>
                  <ml:mult style="default" />
                  <ml:id>cols</ml:id>
                  <ml:id>hsize</ml:id>
                </ml:apply>
              </ml:range>
              <ml:localDefine>
                <ml:apply>
                  <ml:indexer />
                  <ml:id>Q</ml:id>
                  <ml:sequence>
                    <ml:apply>
                      <ml:mult style="default" />
                      <ml:id>levels</ml:id>
                      <ml:id>vsize</ml:id>
                    </ml:apply>
                    <ml:id>j</ml:id>
                  </ml:sequence>
                </ml:apply>
                <ml:real>0</ml:real>
              </ml:localDefine>
            </ml:for>
            <ml:id>Q</ml:id>
          </ml:program>
        </ml:define>
      </math>
      <indexes>
        <phrase>pgridplot function</phrase>
      </indexes>
      <rendering item-idref="14" />
    </region>
    <region region-id="4961" left="6" top="1875" width="441.75" height="159" align-x="172.5" align-y="1884" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="">
      <math optimize="false" export="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id>BasisDisplayPacket2d</ml:id>
            <ml:boundVars>
              <ml:id>b</ml:id>
              <ml:id>level</ml:id>
              <ml:id>row</ml:id>
              <ml:id>col</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:program>
            <ml:localDefine>
              <ml:id>Q</ml:id>
              <ml:apply>
                <ml:id>basis_display2d</ml:id>
                <ml:id>b</ml:id>
              </ml:apply>
            </ml:localDefine>
            <ml:localDefine>
              <ml:id>Grows</ml:id>
              <ml:apply>
                <ml:id>rows</ml:id>
                <ml:id>Q</ml:id>
              </ml:apply>
            </ml:localDefine>
            <ml:localDefine>
              <ml:id>Gcols</ml:id>
              <ml:apply>
                <ml:id>cols</ml:id>
                <ml:id>Q</ml:id>
              </ml:apply>
            </ml:localDefine>
            <ml:for>
              <ml:id>i</ml:id>
              <ml:range>
                <ml:sequence>
                  <ml:apply>
                    <ml:mult style="default" />
                    <ml:id>Gcols</ml:id>
                    <ml:apply>
                      <ml:div />
                      <ml:id>col</ml:id>
                      <ml:apply>
                        <ml:pow />
                        <ml:real>2</ml:real>
                        <ml:id>level</ml:id>
                      </ml:apply>
                    </ml:apply>
                  </ml:apply>
                  <ml:apply>
                    <ml:plus />
                    <ml:apply>
                      <ml:mult style="default" />
                      <ml:apply>
                        <ml:div />
                        <ml:id>col</ml:id>
                        <ml:apply>
                          <ml:pow />
                          <ml:real>2</ml:real>
                          <ml:id>level</ml:id>
                        </ml:apply>
                      </ml:apply>
                      <ml:id>Gcols</ml:id>
                    </ml:apply>
                    <ml:real>2</ml:real>
                  </ml:apply>
                </ml:sequence>
                <ml:apply>
                  <ml:minus />
                  <ml:apply>
                    <ml:mult style="default" />
                    <ml:id>Gcols</ml:id>
                    <ml:apply>
                      <ml:div />
                      <ml:apply>
                        <ml:plus />
                        <ml:id>col</ml:id>
                        <ml:real>1</ml:real>
                      </ml:apply>
                      <ml:apply>
                        <ml:pow />
                        <ml:real>2</ml:real>
                        <ml:id>level</ml:id>
                      </ml:apply>
                    </ml:apply>
                  </ml:apply>
                  <ml:real>1</ml:real>
                </ml:apply>
              </ml:range>
              <ml:for>
                <ml:id>j</ml:id>
                <ml:range>
                  <ml:sequence>
                    <ml:apply>
                      <ml:mult style="default" />
                      <ml:id>Grows</ml:id>
                      <ml:apply>
                        <ml:div />
                        <ml:id>row</ml:id>
                        <ml:apply>
                          <ml:pow />
                          <ml:real>2</ml:real>
                          <ml:id>level</ml:id>
                        </ml:apply>
                      </ml:apply>
                    </ml:apply>
                    <ml:apply>
                      <ml:plus />
                      <ml:apply>
                        <ml:mult style="default" />
                        <ml:apply>
                          <ml:div />
                          <ml:id>row</ml:id>
                          <ml:apply>
                            <ml:pow />
                            <ml:real>2</ml:real>
                            <ml:id>level</ml:id>
                          </ml:apply>
                        </ml:apply>
                        <ml:id>Grows</ml:id>
                      </ml:apply>
                      <ml:real>2</ml:real>
                    </ml:apply>
                  </ml:sequence>
                  <ml:apply>
                    <ml:minus />
                    <ml:apply>
                      <ml:mult style="default" />
                      <ml:id>Grows</ml:id>
                      <ml:apply>
                        <ml:div />
                        <ml:apply>
                          <ml:plus />
                          <ml:id>row</ml:id>
                          <ml:real>1</ml:real>
                        </ml:apply>
                        <ml:apply>
                          <ml:pow />
                          <ml:real>2</ml:real>
                          <ml:id>level</ml:id>
                        </ml:apply>
                      </ml:apply>
                    </ml:apply>
                    <ml:real>1</ml:real>
                  </ml:apply>
                </ml:range>
                <ml:localDefine>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>Q</ml:id>
                    <ml:sequence>
                      <ml:id>j</ml:id>
                      <ml:id>i</ml:id>
                    </ml:sequence>
                  </ml:apply>
                  <ml:real>1</ml:real>
                </ml:localDefine>
              </ml:for>
            </ml:for>
            <ml:id>Q</ml:id>
          </ml:program>
        </ml:define>
      </math>
      <indexes>
        <phrase>BasisDisplayPacket2d function</phrase>
      </indexes>
      <rendering item-idref="15" />
    </region>
    <region region-id="4962" left="0" top="2040" width="6000" height="6" align-x="0" align-y="2040" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="">
      <pageBreak />
    </region>
    <region region-id="4916" left="6" top="2061" width="233.25" height="160.5" align-x="66.75" align-y="2070" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="">
      <math optimize="false" export="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id>wavesort</ml:id>
            <ml:boundVars>
              <ml:id>W</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:program>
            <ml:localDefine>
              <ml:id>q</ml:id>
              <ml:real>0</ml:real>
            </ml:localDefine>
            <ml:for>
              <ml:id>r</ml:id>
              <ml:range>
                <ml:real>0</ml:real>
                <ml:apply>
                  <ml:minus />
                  <ml:apply>
                    <ml:id>rows</ml:id>
                    <ml:id>W</ml:id>
                  </ml:apply>
                  <ml:real>1</ml:real>
                </ml:apply>
              </ml:range>
              <ml:for>
                <ml:id>c</ml:id>
                <ml:range>
                  <ml:real>0</ml:real>
                  <ml:apply>
                    <ml:minus />
                    <ml:apply>
                      <ml:id>cols</ml:id>
                      <ml:id>W</ml:id>
                    </ml:apply>
                    <ml:real>1</ml:real>
                  </ml:apply>
                </ml:range>
                <ml:program>
                  <ml:localDefine>
                    <ml:apply>
                      <ml:indexer />
                      <ml:id>WS</ml:id>
                      <ml:sequence>
                        <ml:id>q</ml:id>
                        <ml:real>0</ml:real>
                      </ml:sequence>
                    </ml:apply>
                    <ml:apply>
                      <ml:absval />
                      <ml:apply>
                        <ml:indexer />
                        <ml:id>W</ml:id>
                        <ml:sequence>
                          <ml:id>r</ml:id>
                          <ml:id>c</ml:id>
                        </ml:sequence>
                      </ml:apply>
                    </ml:apply>
                  </ml:localDefine>
                  <ml:localDefine>
                    <ml:apply>
                      <ml:indexer />
                      <ml:id>WS</ml:id>
                      <ml:sequence>
                        <ml:id>q</ml:id>
                        <ml:real>1</ml:real>
                      </ml:sequence>
                    </ml:apply>
                    <ml:id>r</ml:id>
                  </ml:localDefine>
                  <ml:localDefine>
                    <ml:apply>
                      <ml:indexer />
                      <ml:id>WS</ml:id>
                      <ml:sequence>
                        <ml:id>q</ml:id>
                        <ml:real>2</ml:real>
                      </ml:sequence>
                    </ml:apply>
                    <ml:id>c</ml:id>
                  </ml:localDefine>
                  <ml:localDefine>
                    <ml:id>q</ml:id>
                    <ml:apply>
                      <ml:plus />
                      <ml:id>q</ml:id>
                      <ml:real>1</ml:real>
                    </ml:apply>
                  </ml:localDefine>
                </ml:program>
              </ml:for>
            </ml:for>
            <ml:localDefine>
              <ml:id>WS</ml:id>
              <ml:apply>
                <ml:id>reverse</ml:id>
                <ml:apply>
                  <ml:id>csort</ml:id>
                  <ml:sequence>
                    <ml:id>WS</ml:id>
                    <ml:real>0</ml:real>
                  </ml:sequence>
                </ml:apply>
              </ml:apply>
            </ml:localDefine>
            <ml:apply>
              <ml:id>submatrix</ml:id>
              <ml:sequence>
                <ml:id>WS</ml:id>
                <ml:real>0</ml:real>
                <ml:apply>
                  <ml:minus />
                  <ml:apply>
                    <ml:id>rows</ml:id>
                    <ml:id>WS</ml:id>
                  </ml:apply>
                  <ml:real>1</ml:real>
                </ml:apply>
                <ml:real>1</ml:real>
                <ml:real>2</ml:real>
              </ml:sequence>
            </ml:apply>
          </ml:program>
        </ml:define>
      </math>
      <indexes>
        <phrase>wavesort function</phrase>
      </indexes>
      <rendering item-idref="16" />
    </region>
    <region region-id="4917" left="6" top="2259" width="291.75" height="107.25" align-x="83.25" align-y="2268" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="">
      <math optimize="false" export="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id>shrink</ml:id>
            <ml:boundVars>
              <ml:id>WS</ml:id>
              <ml:id>n</ml:id>
              <ml:id>W</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:program>
            <ml:localDefine>
              <ml:apply>
                <ml:indexer />
                <ml:id>M</ml:id>
                <ml:sequence>
                  <ml:apply>
                    <ml:minus />
                    <ml:apply>
                      <ml:id>rows</ml:id>
                      <ml:id>W</ml:id>
                    </ml:apply>
                    <ml:real>1</ml:real>
                  </ml:apply>
                  <ml:apply>
                    <ml:minus />
                    <ml:apply>
                      <ml:id>cols</ml:id>
                      <ml:id>W</ml:id>
                    </ml:apply>
                    <ml:real>1</ml:real>
                  </ml:apply>
                </ml:sequence>
              </ml:apply>
              <ml:real>0</ml:real>
            </ml:localDefine>
            <ml:localDefine>
              <ml:id>q</ml:id>
              <ml:real>0</ml:real>
            </ml:localDefine>
            <ml:while>
              <ml:apply>
                <ml:lessThan />
                <ml:id>q</ml:id>
                <ml:id>n</ml:id>
              </ml:apply>
              <ml:program>
                <ml:localDefine>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>M</ml:id>
                    <ml:sequence>
                      <ml:parens>
                        <ml:apply>
                          <ml:indexer />
                          <ml:id>WS</ml:id>
                          <ml:sequence>
                            <ml:id>q</ml:id>
                            <ml:real>0</ml:real>
                          </ml:sequence>
                        </ml:apply>
                      </ml:parens>
                      <ml:parens>
                        <ml:apply>
                          <ml:indexer />
                          <ml:id>WS</ml:id>
                          <ml:sequence>
                            <ml:id>q</ml:id>
                            <ml:real>1</ml:real>
                          </ml:sequence>
                        </ml:apply>
                      </ml:parens>
                    </ml:sequence>
                  </ml:apply>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>W</ml:id>
                    <ml:sequence>
                      <ml:parens>
                        <ml:apply>
                          <ml:indexer />
                          <ml:id>WS</ml:id>
                          <ml:sequence>
                            <ml:id>q</ml:id>
                            <ml:real>0</ml:real>
                          </ml:sequence>
                        </ml:apply>
                      </ml:parens>
                      <ml:parens>
                        <ml:apply>
                          <ml:indexer />
                          <ml:id>WS</ml:id>
                          <ml:sequence>
                            <ml:id>q</ml:id>
                            <ml:real>1</ml:real>
                          </ml:sequence>
                        </ml:apply>
                      </ml:parens>
                    </ml:sequence>
                  </ml:apply>
                </ml:localDefine>
                <ml:localDefine>
                  <ml:id>q</ml:id>
                  <ml:apply>
                    <ml:plus />
                    <ml:id>q</ml:id>
                    <ml:real>1</ml:real>
                  </ml:apply>
                </ml:localDefine>
              </ml:program>
            </ml:while>
            <ml:id>M</ml:id>
          </ml:program>
        </ml:define>
      </math>
      <indexes>
        <phrase>shrink function</phrase>
      </indexes>
      <rendering item-idref="17" />
    </region>
    <region region-id="4918" left="6" top="2397" width="314.25" height="152.25" align-x="126.75" align-y="2406" show-border="false" show-highlight="false" is-protected="true" background-color="#ff8000" tag="">
      <math optimize="false" export="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id>wavedecomp2d</ml:id>
            <ml:boundVars>
              <ml:id>x</ml:id>
              <ml:id>J</ml:id>
              <ml:id>n</ml:id>
              <ml:id>filter</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:program>
            <ml:localDefine>
              <ml:id>W</ml:id>
              <ml:apply>
                <ml:id>dwt</ml:id>
                <ml:sequence>
                  <ml:id>x</ml:id>
                  <ml:id>J</ml:id>
                  <ml:id>filter</ml:id>
                </ml:sequence>
              </ml:apply>
            </ml:localDefine>
            <ml:localDefine>
              <ml:id>L</ml:id>
              <ml:apply>
                <ml:id>wavesort</ml:id>
                <ml:id>W</ml:id>
              </ml:apply>
            </ml:localDefine>
            <ml:localDefine>
              <ml:apply>
                <ml:indexer />
                <ml:id>wt</ml:id>
                <ml:sequence>
                  <ml:apply>
                    <ml:minus />
                    <ml:apply>
                      <ml:id>rows</ml:id>
                      <ml:id>W</ml:id>
                    </ml:apply>
                    <ml:real>1</ml:real>
                  </ml:apply>
                  <ml:apply>
                    <ml:minus />
                    <ml:apply>
                      <ml:id>cols</ml:id>
                      <ml:id>W</ml:id>
                    </ml:apply>
                    <ml:real>1</ml:real>
                  </ml:apply>
                </ml:sequence>
              </ml:apply>
              <ml:real>0</ml:real>
            </ml:localDefine>
            <ml:for>
              <ml:id>qq</ml:id>
              <ml:range>
                <ml:real>0</ml:real>
                <ml:apply>
                  <ml:minus />
                  <ml:id>n</ml:id>
                  <ml:real>1</ml:real>
                </ml:apply>
              </ml:range>
              <ml:program>
                <ml:localDefine>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>wt</ml:id>
                    <ml:sequence>
                      <ml:parens>
                        <ml:apply>
                          <ml:indexer />
                          <ml:id>L</ml:id>
                          <ml:sequence>
                            <ml:id>qq</ml:id>
                            <ml:real>0</ml:real>
                          </ml:sequence>
                        </ml:apply>
                      </ml:parens>
                      <ml:parens>
                        <ml:apply>
                          <ml:indexer />
                          <ml:id>L</ml:id>
                          <ml:sequence>
                            <ml:id>qq</ml:id>
                            <ml:real>1</ml:real>
                          </ml:sequence>
                        </ml:apply>
                      </ml:parens>
                    </ml:sequence>
                  </ml:apply>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>W</ml:id>
                    <ml:sequence>
                      <ml:parens>
                        <ml:apply>
                          <ml:indexer />
                          <ml:id>L</ml:id>
                          <ml:sequence>
                            <ml:id>qq</ml:id>
                            <ml:real>0</ml:real>
                          </ml:sequence>
                        </ml:apply>
                      </ml:parens>
                      <ml:parens>
                        <ml:apply>
                          <ml:indexer />
                          <ml:id>L</ml:id>
                          <ml:sequence>
                            <ml:id>qq</ml:id>
                            <ml:real>1</ml:real>
                          </ml:sequence>
                        </ml:apply>
                      </ml:parens>
                    </ml:sequence>
                  </ml:apply>
                </ml:localDefine>
                <ml:localDefine>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>R</ml:id>
                    <ml:id>qq</ml:id>
                  </ml:apply>
                  <ml:apply>
                    <ml:id>idwt</ml:id>
                    <ml:sequence>
                      <ml:id>wt</ml:id>
                      <ml:id>J</ml:id>
                      <ml:id>filter</ml:id>
                    </ml:sequence>
                  </ml:apply>
                </ml:localDefine>
                <ml:localDefine>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>wt</ml:id>
                    <ml:sequence>
                      <ml:parens>
                        <ml:apply>
                          <ml:indexer />
                          <ml:id>L</ml:id>
                          <ml:sequence>
                            <ml:id>qq</ml:id>
                            <ml:real>0</ml:real>
                          </ml:sequence>
                        </ml:apply>
                      </ml:parens>
                      <ml:parens>
                        <ml:apply>
                          <ml:indexer />
                          <ml:id>L</ml:id>
                          <ml:sequence>
                            <ml:id>qq</ml:id>
                            <ml:real>1</ml:real>
                          </ml:sequence>
                        </ml:apply>
                      </ml:parens>
                    </ml:sequence>
                  </ml:apply>
                  <ml:real>0</ml:real>
                </ml:localDefine>
              </ml:program>
            </ml:for>
            <ml:id>R</ml:id>
          </ml:program>
        </ml:define>
      </math>
      <indexes>
        <phrase>wavedecomp2d function</phrase>
      </indexes>
      <rendering item-idref="18" />
    </region>
    <region region-id="4919" left="6" top="2571" width="225.75" height="62.25" align-x="123.75" align-y="2580" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="">
      <math optimize="false" export="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id>waveapprox2d</ml:id>
            <ml:boundVars>
              <ml:id>y</ml:id>
              <ml:id>J</ml:id>
              <ml:id>n</ml:id>
              <ml:id>filter</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:program>
            <ml:localDefine>
              <ml:id>W</ml:id>
              <ml:apply>
                <ml:id>dwt</ml:id>
                <ml:sequence>
                  <ml:id>y</ml:id>
                  <ml:id>J</ml:id>
                  <ml:id>filter</ml:id>
                </ml:sequence>
              </ml:apply>
            </ml:localDefine>
            <ml:localDefine>
              <ml:id>L</ml:id>
              <ml:apply>
                <ml:id>wavesort</ml:id>
                <ml:id>W</ml:id>
              </ml:apply>
            </ml:localDefine>
            <ml:localDefine>
              <ml:id>yr</ml:id>
              <ml:apply>
                <ml:id>shrink</ml:id>
                <ml:sequence>
                  <ml:id>L</ml:id>
                  <ml:id>n</ml:id>
                  <ml:id>W</ml:id>
                </ml:sequence>
              </ml:apply>
            </ml:localDefine>
            <ml:apply>
              <ml:id>idwt</ml:id>
              <ml:sequence>
                <ml:id>yr</ml:id>
                <ml:id>J</ml:id>
                <ml:id>filter</ml:id>
              </ml:sequence>
            </ml:apply>
          </ml:program>
        </ml:define>
      </math>
      <indexes>
        <phrase>waveapprox2d function</phrase>
      </indexes>
      <rendering item-idref="19" />
    </region>
    <region region-id="4920" left="6" top="2655" width="273.75" height="51" align-x="83.25" align-y="2664" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="">
      <math optimize="false" export="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id>delta_shrink</ml:id>
            <ml:boundVars>
              <ml:id>v</ml:id>
              <ml:id>c</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:program>
            <ml:for>
              <ml:id>k</ml:id>
              <ml:range>
                <ml:real>0</ml:real>
                <ml:apply>
                  <ml:id>last</ml:id>
                  <ml:id>v</ml:id>
                </ml:apply>
              </ml:range>
              <ml:localDefine>
                <ml:apply>
                  <ml:indexer />
                  <ml:id>v</ml:id>
                  <ml:id>k</ml:id>
                </ml:apply>
                <ml:apply>
                  <ml:id>if</ml:id>
                  <ml:sequence>
                    <ml:apply>
                      <ml:lessThan />
                      <ml:apply>
                        <ml:absval />
                        <ml:apply>
                          <ml:indexer />
                          <ml:id>v</ml:id>
                          <ml:id>k</ml:id>
                        </ml:apply>
                      </ml:apply>
                      <ml:id>c</ml:id>
                    </ml:apply>
                    <ml:real>0</ml:real>
                    <ml:apply>
                      <ml:mult style="default" />
                      <ml:apply>
                        <ml:id>sign</ml:id>
                        <ml:apply>
                          <ml:indexer />
                          <ml:id>v</ml:id>
                          <ml:id>k</ml:id>
                        </ml:apply>
                      </ml:apply>
                      <ml:parens>
                        <ml:apply>
                          <ml:minus />
                          <ml:apply>
                            <ml:absval />
                            <ml:apply>
                              <ml:indexer />
                              <ml:id>v</ml:id>
                              <ml:id>k</ml:id>
                            </ml:apply>
                          </ml:apply>
                          <ml:id>c</ml:id>
                        </ml:apply>
                      </ml:parens>
                    </ml:apply>
                  </ml:sequence>
                </ml:apply>
              </ml:localDefine>
            </ml:for>
            <ml:id>v</ml:id>
          </ml:program>
        </ml:define>
      </math>
      <indexes>
        <phrase>delta_shrink function</phrase>
      </indexes>
      <rendering item-idref="20" />
    </region>
    <region region-id="4922" left="0" top="2724" width="6000" height="6" align-x="0" align-y="2724" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="">
      <pageBreak />
    </region>
    <region region-id="4921" left="6" top="2739" width="240" height="222" align-x="93.75" align-y="2748" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="">
      <math optimize="false" export="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id>waveshrink</ml:id>
            <ml:boundVars>
              <ml:id>y</ml:id>
              <ml:id>filter</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:program>
            <ml:localDefine>
              <ml:id>J</ml:id>
              <ml:apply>
                <ml:id>MaxDWTLevel</ml:id>
                <ml:id>y</ml:id>
              </ml:apply>
            </ml:localDefine>
            <ml:localDefine>
              <ml:id>w</ml:id>
              <ml:apply>
                <ml:id>dwt</ml:id>
                <ml:sequence>
                  <ml:id>y</ml:id>
                  <ml:id>J</ml:id>
                  <ml:id>filter</ml:id>
                </ml:sequence>
              </ml:apply>
            </ml:localDefine>
            <ml:localDefine>
              <ml:id>λ</ml:id>
              <ml:apply>
                <ml:mult style="default" />
                <ml:real>2</ml:real>
                <ml:apply>
                  <ml:id>log</ml:id>
                  <ml:apply>
                    <ml:id>length</ml:id>
                    <ml:id>y</ml:id>
                  </ml:apply>
                </ml:apply>
              </ml:apply>
            </ml:localDefine>
            <ml:localDefine>
              <ml:id>σ</ml:id>
              <ml:apply>
                <ml:id>median</ml:id>
                <ml:apply>
                  <ml:vectorize />
                  <ml:apply>
                    <ml:absval />
                    <ml:apply>
                      <ml:minus />
                      <ml:id>w</ml:id>
                      <ml:apply>
                        <ml:id>median</ml:id>
                        <ml:id>w</ml:id>
                      </ml:apply>
                    </ml:apply>
                  </ml:apply>
                </ml:apply>
              </ml:apply>
            </ml:localDefine>
            <ml:localDefine>
              <ml:id>c</ml:id>
              <ml:apply>
                <ml:mult style="default" />
                <ml:id>λ</ml:id>
                <ml:id>σ</ml:id>
              </ml:apply>
            </ml:localDefine>
            <ml:localDefine>
              <ml:id>Jmax</ml:id>
              <ml:apply>
                <ml:id>if</ml:id>
                <ml:sequence>
                  <ml:apply>
                    <ml:greaterThan />
                    <ml:id>J</ml:id>
                    <ml:real>8</ml:real>
                  </ml:apply>
                  <ml:apply>
                    <ml:minus />
                    <ml:id>J</ml:id>
                    <ml:real>4</ml:real>
                  </ml:apply>
                  <ml:id>J</ml:id>
                </ml:sequence>
              </ml:apply>
            </ml:localDefine>
            <ml:for>
              <ml:id>js</ml:id>
              <ml:range>
                <ml:real>1</ml:real>
                <ml:id>Jmax</ml:id>
              </ml:range>
              <ml:program>
                <ml:localDefine>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>d</ml:id>
                    <ml:id>js</ml:id>
                  </ml:apply>
                  <ml:apply>
                    <ml:id>get_detail</ml:id>
                    <ml:sequence>
                      <ml:id>w</ml:id>
                      <ml:id>js</ml:id>
                    </ml:sequence>
                  </ml:apply>
                </ml:localDefine>
                <ml:localDefine>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>d</ml:id>
                    <ml:id>js</ml:id>
                  </ml:apply>
                  <ml:apply>
                    <ml:id>delta_shrink</ml:id>
                    <ml:sequence>
                      <ml:apply>
                        <ml:indexer />
                        <ml:id>d</ml:id>
                        <ml:id>js</ml:id>
                      </ml:apply>
                      <ml:id>c</ml:id>
                    </ml:sequence>
                  </ml:apply>
                </ml:localDefine>
                <ml:localDefine>
                  <ml:id>w</ml:id>
                  <ml:apply>
                    <ml:id>put_detail</ml:id>
                    <ml:sequence>
                      <ml:id>w</ml:id>
                      <ml:id>js</ml:id>
                      <ml:apply>
                        <ml:indexer />
                        <ml:id>d</ml:id>
                        <ml:id>js</ml:id>
                      </ml:apply>
                    </ml:sequence>
                  </ml:apply>
                </ml:localDefine>
              </ml:program>
            </ml:for>
            <ml:localDefine>
              <ml:id subscript="r">y</ml:id>
              <ml:apply>
                <ml:id>idwt</ml:id>
                <ml:sequence>
                  <ml:id>w</ml:id>
                  <ml:id>J</ml:id>
                  <ml:id>filter</ml:id>
                </ml:sequence>
              </ml:apply>
            </ml:localDefine>
            <ml:id subscript="r">y</ml:id>
          </ml:program>
        </ml:define>
      </math>
      <indexes>
        <phrase>waveshrink function</phrase>
      </indexes>
      <rendering item-idref="21" />
    </region>
    <region region-id="4923" left="6" top="2973.75" width="243" height="204.75" align-x="81.75" align-y="2988" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="">
      <math optimize="false" export="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id>Concentration</ml:id>
            <ml:boundVars>
              <ml:id>v</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:program>
            <ml:localDefine>
              <ml:id>w</ml:id>
              <ml:apply>
                <ml:matcol />
                <ml:id>v</ml:id>
                <ml:real>0</ml:real>
              </ml:apply>
            </ml:localDefine>
            <ml:ifThen>
              <ml:apply>
                <ml:greaterThan />
                <ml:apply>
                  <ml:id>cols</ml:id>
                  <ml:id>v</ml:id>
                </ml:apply>
                <ml:real>1</ml:real>
              </ml:apply>
              <ml:for>
                <ml:id>i</ml:id>
                <ml:range>
                  <ml:real>1</ml:real>
                  <ml:apply>
                    <ml:minus />
                    <ml:apply>
                      <ml:id>cols</ml:id>
                      <ml:id>v</ml:id>
                    </ml:apply>
                    <ml:real>1</ml:real>
                  </ml:apply>
                </ml:range>
                <ml:localDefine>
                  <ml:id>w</ml:id>
                  <ml:apply>
                    <ml:id>stack</ml:id>
                    <ml:sequence>
                      <ml:id>w</ml:id>
                      <ml:apply>
                        <ml:matcol />
                        <ml:id>v</ml:id>
                        <ml:id>i</ml:id>
                      </ml:apply>
                    </ml:sequence>
                  </ml:apply>
                </ml:localDefine>
              </ml:for>
            </ml:ifThen>
            <ml:localDefine>
              <ml:id>w</ml:id>
              <ml:apply>
                <ml:id>reverse</ml:id>
                <ml:apply>
                  <ml:id>sort</ml:id>
                  <ml:apply>
                    <ml:vectorize />
                    <ml:apply>
                      <ml:absval />
                      <ml:id>w</ml:id>
                    </ml:apply>
                  </ml:apply>
                </ml:apply>
              </ml:apply>
            </ml:localDefine>
            <ml:localDefine>
              <ml:id>totalEnergy</ml:id>
              <ml:apply>
                <ml:mult style="default" />
                <ml:id>w</ml:id>
                <ml:id>w</ml:id>
              </ml:apply>
            </ml:localDefine>
            <ml:localDefine>
              <ml:apply>
                <ml:indexer />
                <ml:id>w</ml:id>
                <ml:real>0</ml:real>
              </ml:apply>
              <ml:apply>
                <ml:pow />
                <ml:parens>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>w</ml:id>
                    <ml:real>0</ml:real>
                  </ml:apply>
                </ml:parens>
                <ml:real>2</ml:real>
              </ml:apply>
            </ml:localDefine>
            <ml:for>
              <ml:id>i</ml:id>
              <ml:range>
                <ml:real>1</ml:real>
                <ml:apply>
                  <ml:minus />
                  <ml:apply>
                    <ml:id>rows</ml:id>
                    <ml:id>w</ml:id>
                  </ml:apply>
                  <ml:real>1</ml:real>
                </ml:apply>
              </ml:range>
              <ml:localDefine>
                <ml:apply>
                  <ml:indexer />
                  <ml:id>w</ml:id>
                  <ml:id>i</ml:id>
                </ml:apply>
                <ml:apply>
                  <ml:plus />
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>w</ml:id>
                    <ml:apply>
                      <ml:minus />
                      <ml:id>i</ml:id>
                      <ml:real>1</ml:real>
                    </ml:apply>
                  </ml:apply>
                  <ml:apply>
                    <ml:pow />
                    <ml:parens>
                      <ml:apply>
                        <ml:indexer />
                        <ml:id>w</ml:id>
                        <ml:id>i</ml:id>
                      </ml:apply>
                    </ml:parens>
                    <ml:real>2</ml:real>
                  </ml:apply>
                </ml:apply>
              </ml:localDefine>
            </ml:for>
            <ml:apply>
              <ml:vectorize />
              <ml:apply>
                <ml:div />
                <ml:id>w</ml:id>
                <ml:id>totalEnergy</ml:id>
              </ml:apply>
            </ml:apply>
          </ml:program>
        </ml:define>
      </math>
      <indexes>
        <phrase>Concentration function</phrase>
      </indexes>
      <rendering item-idref="22" />
    </region>
    <region region-id="4613" left="0" top="3192" width="6000" height="6" align-x="0" align-y="3192" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="">
      <pageBreak />
    </region>
    <region region-id="4468" left="6" top="3204.75" width="192" height="14.25" align-x="6" align-y="3216" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Heading 1" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">2D Multiresolution Analysis Functions</p>
      </text>
      <indexes>
        <phrase>2D multiresolution analysis functions</phrase>
      </indexes>
    </region>
    <region region-id="4924" left="6" top="3225" width="404.25" height="255" align-x="79.5" align-y="3234" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="">
      <math optimize="false" export="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id>mra2d</ml:id>
            <ml:boundVars>
              <ml:id>v</ml:id>
              <ml:id>J</ml:id>
              <ml:id>filter</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:program>
            <ml:localDefine>
              <ml:id>w</ml:id>
              <ml:apply>
                <ml:id>dwt</ml:id>
                <ml:sequence>
                  <ml:id>v</ml:id>
                  <ml:id>J</ml:id>
                  <ml:id>filter</ml:id>
                </ml:sequence>
              </ml:apply>
            </ml:localDefine>
            <ml:for>
              <ml:id>ii</ml:id>
              <ml:range>
                <ml:real>0</ml:real>
                <ml:apply>
                  <ml:minus />
                  <ml:apply>
                    <ml:id>rows</ml:id>
                    <ml:id>v</ml:id>
                  </ml:apply>
                  <ml:real>1</ml:real>
                </ml:apply>
              </ml:range>
              <ml:for>
                <ml:id>jj</ml:id>
                <ml:range>
                  <ml:real>0</ml:real>
                  <ml:apply>
                    <ml:minus />
                    <ml:apply>
                      <ml:id>cols</ml:id>
                      <ml:id>v</ml:id>
                    </ml:apply>
                    <ml:real>1</ml:real>
                  </ml:apply>
                </ml:range>
                <ml:localDefine>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>Z</ml:id>
                    <ml:sequence>
                      <ml:id>ii</ml:id>
                      <ml:id>jj</ml:id>
                    </ml:sequence>
                  </ml:apply>
                  <ml:real>0</ml:real>
                </ml:localDefine>
              </ml:for>
            </ml:for>
            <ml:localDefine>
              <ml:apply>
                <ml:indexer />
                <ml:id>D</ml:id>
                <ml:real>0</ml:real>
              </ml:apply>
              <ml:apply>
                <ml:id>idwt</ml:id>
                <ml:sequence>
                  <ml:apply>
                    <ml:id>put_smooth2d</ml:id>
                    <ml:sequence>
                      <ml:id>Z</ml:id>
                      <ml:id>J</ml:id>
                      <ml:apply>
                        <ml:id>get_smooth2d</ml:id>
                        <ml:sequence>
                          <ml:id>w</ml:id>
                          <ml:id>J</ml:id>
                        </ml:sequence>
                      </ml:apply>
                    </ml:sequence>
                  </ml:apply>
                  <ml:id>J</ml:id>
                  <ml:id>filter</ml:id>
                </ml:sequence>
              </ml:apply>
            </ml:localDefine>
            <ml:for>
              <ml:id>qj</ml:id>
              <ml:range>
                <ml:id>J</ml:id>
                <ml:real>1</ml:real>
              </ml:range>
              <ml:program>
                <ml:for>
                  <ml:id>ii</ml:id>
                  <ml:range>
                    <ml:real>0</ml:real>
                    <ml:apply>
                      <ml:minus />
                      <ml:apply>
                        <ml:id>rows</ml:id>
                        <ml:id>v</ml:id>
                      </ml:apply>
                      <ml:real>1</ml:real>
                    </ml:apply>
                  </ml:range>
                  <ml:for>
                    <ml:id>jj</ml:id>
                    <ml:range>
                      <ml:real>0</ml:real>
                      <ml:apply>
                        <ml:minus />
                        <ml:apply>
                          <ml:id>cols</ml:id>
                          <ml:id>v</ml:id>
                        </ml:apply>
                        <ml:real>1</ml:real>
                      </ml:apply>
                    </ml:range>
                    <ml:localDefine>
                      <ml:apply>
                        <ml:indexer />
                        <ml:id>Z</ml:id>
                        <ml:sequence>
                          <ml:id>ii</ml:id>
                          <ml:id>jj</ml:id>
                        </ml:sequence>
                      </ml:apply>
                      <ml:real>0</ml:real>
                    </ml:localDefine>
                  </ml:for>
                </ml:for>
                <ml:localDefine>
                  <ml:id subscript="H">M</ml:id>
                  <ml:apply>
                    <ml:id>put_detail2d</ml:id>
                    <ml:sequence>
                      <ml:id>Z</ml:id>
                      <ml:id>qj</ml:id>
                      <ml:apply>
                        <ml:id>get_detail2d</ml:id>
                        <ml:sequence>
                          <ml:id>w</ml:id>
                          <ml:id>qj</ml:id>
                          <ml:str>H</ml:str>
                        </ml:sequence>
                      </ml:apply>
                      <ml:str>H</ml:str>
                    </ml:sequence>
                  </ml:apply>
                </ml:localDefine>
                <ml:localDefine>
                  <ml:id subscript="V">M</ml:id>
                  <ml:apply>
                    <ml:id>put_detail2d</ml:id>
                    <ml:sequence>
                      <ml:id>Z</ml:id>
                      <ml:id>qj</ml:id>
                      <ml:apply>
                        <ml:id>get_detail2d</ml:id>
                        <ml:sequence>
                          <ml:id>w</ml:id>
                          <ml:id>qj</ml:id>
                          <ml:str>V</ml:str>
                        </ml:sequence>
                      </ml:apply>
                      <ml:str>V</ml:str>
                    </ml:sequence>
                  </ml:apply>
                </ml:localDefine>
                <ml:localDefine>
                  <ml:id subscript="D">M</ml:id>
                  <ml:apply>
                    <ml:id>put_detail2d</ml:id>
                    <ml:sequence>
                      <ml:id>Z</ml:id>
                      <ml:id>qj</ml:id>
                      <ml:apply>
                        <ml:id>get_detail2d</ml:id>
                        <ml:sequence>
                          <ml:id>w</ml:id>
                          <ml:id>qj</ml:id>
                          <ml:str>D</ml:str>
                        </ml:sequence>
                      </ml:apply>
                      <ml:str>D</ml:str>
                    </ml:sequence>
                  </ml:apply>
                </ml:localDefine>
                <ml:localDefine>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>D</ml:id>
                    <ml:apply>
                      <ml:minus />
                      <ml:apply>
                        <ml:plus />
                        <ml:id>J</ml:id>
                        <ml:real>1</ml:real>
                      </ml:apply>
                      <ml:id>qj</ml:id>
                    </ml:apply>
                  </ml:apply>
                  <ml:apply>
                    <ml:plus />
                    <ml:apply>
                      <ml:plus />
                      <ml:apply>
                        <ml:id>idwt</ml:id>
                        <ml:sequence>
                          <ml:id subscript="H">M</ml:id>
                          <ml:id>J</ml:id>
                          <ml:id>filter</ml:id>
                        </ml:sequence>
                      </ml:apply>
                      <ml:apply>
                        <ml:id>idwt</ml:id>
                        <ml:sequence>
                          <ml:id subscript="V">M</ml:id>
                          <ml:id>J</ml:id>
                          <ml:id>filter</ml:id>
                        </ml:sequence>
                      </ml:apply>
                    </ml:apply>
                    <ml:apply>
                      <ml:id>idwt</ml:id>
                      <ml:sequence>
                        <ml:id subscript="D">M</ml:id>
                        <ml:id>J</ml:id>
                        <ml:id>filter</ml:id>
                      </ml:sequence>
                    </ml:apply>
                  </ml:apply>
                </ml:localDefine>
              </ml:program>
            </ml:for>
            <ml:id>D</ml:id>
          </ml:program>
        </ml:define>
      </math>
      <indexes>
        <phrase>mra2d function</phrase>
      </indexes>
      <rendering item-idref="23" />
    </region>
    <region region-id="4925" left="6" top="3489" width="201" height="89.25" align-x="102" align-y="3498" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="">
      <math optimize="false" export="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id>mrapprox2d</ml:id>
            <ml:boundVars>
              <ml:id>y</ml:id>
              <ml:id>J</ml:id>
              <ml:id>filter</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:program>
            <ml:localDefine>
              <ml:id>D</ml:id>
              <ml:apply>
                <ml:id>mra2d</ml:id>
                <ml:sequence>
                  <ml:id>y</ml:id>
                  <ml:id>J</ml:id>
                  <ml:id>filter</ml:id>
                </ml:sequence>
              </ml:apply>
            </ml:localDefine>
            <ml:localDefine>
              <ml:apply>
                <ml:indexer />
                <ml:id>S</ml:id>
                <ml:real>0</ml:real>
              </ml:apply>
              <ml:apply>
                <ml:indexer />
                <ml:id>D</ml:id>
                <ml:real>0</ml:real>
              </ml:apply>
            </ml:localDefine>
            <ml:for>
              <ml:id>j</ml:id>
              <ml:range>
                <ml:real>1</ml:real>
                <ml:id>J</ml:id>
              </ml:range>
              <ml:localDefine>
                <ml:apply>
                  <ml:indexer />
                  <ml:id>S</ml:id>
                  <ml:id>j</ml:id>
                </ml:apply>
                <ml:apply>
                  <ml:plus />
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>S</ml:id>
                    <ml:apply>
                      <ml:minus />
                      <ml:id>j</ml:id>
                      <ml:real>1</ml:real>
                    </ml:apply>
                  </ml:apply>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>D</ml:id>
                    <ml:id>j</ml:id>
                  </ml:apply>
                </ml:apply>
              </ml:localDefine>
            </ml:for>
            <ml:id>S</ml:id>
          </ml:program>
        </ml:define>
      </math>
      <indexes>
        <phrase>mrapprox2d function</phrase>
      </indexes>
      <rendering item-idref="24" />
    </region>
    <region region-id="4614" left="0" top="3582" width="6000" height="6" align-x="0" align-y="3582" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="">
      <pageBreak />
    </region>
    <region region-id="4471" left="6" top="3594.75" width="178.5" height="14.25" align-x="6" align-y="3606" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Heading 1" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Time-Frequency Analysis Functions</p>
      </text>
      <indexes>
        <phrase>time-frequency analysis functions</phrase>
      </indexes>
    </region>
    <region region-id="4926" left="6" top="3621" width="390.75" height="289.5" align-x="161.25" align-y="3630" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="">
      <math optimize="false" export="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id>tfPlotFromLCT</ml:id>
            <ml:boundVars>
              <ml:id>w</ml:id>
              <ml:id>basis</ml:id>
              <ml:id>hsize</ml:id>
              <ml:id>vsize</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:program>
            <ml:localDefine>
              <ml:id>N</ml:id>
              <ml:apply>
                <ml:id>rows</ml:id>
                <ml:id>w</ml:id>
              </ml:apply>
            </ml:localDefine>
            <ml:localDefine>
              <ml:id>vextent</ml:id>
              <ml:apply>
                <ml:mult style="default" />
                <ml:id>N</ml:id>
                <ml:id>vsize</ml:id>
              </ml:apply>
            </ml:localDefine>
            <ml:localDefine>
              <ml:apply>
                <ml:indexer />
                <ml:id>Q</ml:id>
                <ml:sequence>
                  <ml:apply>
                    <ml:minus />
                    <ml:id>vextent</ml:id>
                    <ml:real>1</ml:real>
                  </ml:apply>
                  <ml:apply>
                    <ml:minus />
                    <ml:apply>
                      <ml:mult style="default" />
                      <ml:id>N</ml:id>
                      <ml:id>hsize</ml:id>
                    </ml:apply>
                    <ml:real>1</ml:real>
                  </ml:apply>
                </ml:sequence>
              </ml:apply>
              <ml:real>0</ml:real>
            </ml:localDefine>
            <ml:for>
              <ml:id>r</ml:id>
              <ml:range>
                <ml:real>0</ml:real>
                <ml:apply>
                  <ml:minus />
                  <ml:apply>
                    <ml:id>rows</ml:id>
                    <ml:id>basis</ml:id>
                  </ml:apply>
                  <ml:real>1</ml:real>
                </ml:apply>
              </ml:range>
              <ml:program>
                <ml:localDefine>
                  <ml:id>j</ml:id>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>basis</ml:id>
                    <ml:sequence>
                      <ml:id>r</ml:id>
                      <ml:real>0</ml:real>
                    </ml:sequence>
                  </ml:apply>
                </ml:localDefine>
                <ml:localDefine>
                  <ml:id>b</ml:id>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>basis</ml:id>
                    <ml:sequence>
                      <ml:id>r</ml:id>
                      <ml:real>1</ml:real>
                    </ml:sequence>
                  </ml:apply>
                </ml:localDefine>
                <ml:localDefine>
                  <ml:id>ttj</ml:id>
                  <ml:apply>
                    <ml:pow />
                    <ml:real>2</ml:real>
                    <ml:id>j</ml:id>
                  </ml:apply>
                </ml:localDefine>
                <ml:localDefine>
                  <ml:id>packet</ml:id>
                  <ml:apply>
                    <ml:id>get_subband</ml:id>
                    <ml:sequence>
                      <ml:id>w</ml:id>
                      <ml:id>j</ml:id>
                      <ml:id>b</ml:id>
                    </ml:sequence>
                  </ml:apply>
                </ml:localDefine>
                <ml:for>
                  <ml:id>k</ml:id>
                  <ml:range>
                    <ml:real>0</ml:real>
                    <ml:apply>
                      <ml:minus />
                      <ml:apply>
                        <ml:div />
                        <ml:id>N</ml:id>
                        <ml:id>ttj</ml:id>
                      </ml:apply>
                      <ml:real>1</ml:real>
                    </ml:apply>
                  </ml:range>
                  <ml:program>
                    <ml:localDefine>
                      <ml:id>coeff</ml:id>
                      <ml:apply>
                        <ml:indexer />
                        <ml:id>packet</ml:id>
                        <ml:id>k</ml:id>
                      </ml:apply>
                    </ml:localDefine>
                    <ml:for>
                      <ml:id>x</ml:id>
                      <ml:range>
                        <ml:apply>
                          <ml:mult style="default" />
                          <ml:apply>
                            <ml:mult style="default" />
                            <ml:id>hsize</ml:id>
                            <ml:id>N</ml:id>
                          </ml:apply>
                          <ml:apply>
                            <ml:div />
                            <ml:id>b</ml:id>
                            <ml:id>ttj</ml:id>
                          </ml:apply>
                        </ml:apply>
                        <ml:apply>
                          <ml:minus />
                          <ml:apply>
                            <ml:mult style="default" />
                            <ml:apply>
                              <ml:mult style="default" />
                              <ml:id>hsize</ml:id>
                              <ml:id>N</ml:id>
                            </ml:apply>
                            <ml:apply>
                              <ml:div />
                              <ml:apply>
                                <ml:plus />
                                <ml:id>b</ml:id>
                                <ml:real>1</ml:real>
                              </ml:apply>
                              <ml:id>ttj</ml:id>
                            </ml:apply>
                          </ml:apply>
                          <ml:real>1</ml:real>
                        </ml:apply>
                      </ml:range>
                      <ml:for>
                        <ml:id>y</ml:id>
                        <ml:range>
                          <ml:apply>
                            <ml:mult style="default" />
                            <ml:apply>
                              <ml:mult style="default" />
                              <ml:id>vsize</ml:id>
                              <ml:id>ttj</ml:id>
                            </ml:apply>
                            <ml:id>k</ml:id>
                          </ml:apply>
                          <ml:apply>
                            <ml:minus />
                            <ml:apply>
                              <ml:mult style="default" />
                              <ml:apply>
                                <ml:mult style="default" />
                                <ml:id>vsize</ml:id>
                                <ml:id>ttj</ml:id>
                              </ml:apply>
                              <ml:parens>
                                <ml:apply>
                                  <ml:plus />
                                  <ml:id>k</ml:id>
                                  <ml:real>1</ml:real>
                                </ml:apply>
                              </ml:parens>
                            </ml:apply>
                            <ml:real>1</ml:real>
                          </ml:apply>
                        </ml:range>
                        <ml:localDefine>
                          <ml:apply>
                            <ml:indexer />
                            <ml:id>Q</ml:id>
                            <ml:sequence>
                              <ml:apply>
                                <ml:minus />
                                <ml:apply>
                                  <ml:minus />
                                  <ml:id>vextent</ml:id>
                                  <ml:real>1</ml:real>
                                </ml:apply>
                                <ml:id>y</ml:id>
                              </ml:apply>
                              <ml:id>x</ml:id>
                            </ml:sequence>
                          </ml:apply>
                          <ml:apply>
                            <ml:absval />
                            <ml:id>coeff</ml:id>
                          </ml:apply>
                        </ml:localDefine>
                      </ml:for>
                    </ml:for>
                  </ml:program>
                </ml:for>
              </ml:program>
            </ml:for>
            <ml:apply>
              <ml:minus />
              <ml:real>255</ml:real>
              <ml:apply>
                <ml:id>scale</ml:id>
                <ml:id>Q</ml:id>
              </ml:apply>
            </ml:apply>
          </ml:program>
        </ml:define>
      </math>
      <indexes>
        <phrase>tfPlotFromLCT function</phrase>
      </indexes>
      <rendering item-idref="25" />
    </region>
    <region region-id="4927" left="6" top="3927" width="396" height="289.5" align-x="165" align-y="3936" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="">
      <math optimize="false" export="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id>tfPlotFromWPT</ml:id>
            <ml:boundVars>
              <ml:id>w</ml:id>
              <ml:id>basis</ml:id>
              <ml:id>hsize</ml:id>
              <ml:id>vsize</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:program>
            <ml:localDefine>
              <ml:id>N</ml:id>
              <ml:apply>
                <ml:id>rows</ml:id>
                <ml:id>w</ml:id>
              </ml:apply>
            </ml:localDefine>
            <ml:localDefine>
              <ml:id>vextent</ml:id>
              <ml:apply>
                <ml:mult style="default" />
                <ml:id>N</ml:id>
                <ml:id>vsize</ml:id>
              </ml:apply>
            </ml:localDefine>
            <ml:localDefine>
              <ml:apply>
                <ml:indexer />
                <ml:id>Q</ml:id>
                <ml:sequence>
                  <ml:apply>
                    <ml:minus />
                    <ml:id>vextent</ml:id>
                    <ml:real>1</ml:real>
                  </ml:apply>
                  <ml:apply>
                    <ml:minus />
                    <ml:apply>
                      <ml:mult style="default" />
                      <ml:id>N</ml:id>
                      <ml:id>hsize</ml:id>
                    </ml:apply>
                    <ml:real>1</ml:real>
                  </ml:apply>
                </ml:sequence>
              </ml:apply>
              <ml:real>0</ml:real>
            </ml:localDefine>
            <ml:for>
              <ml:id>r</ml:id>
              <ml:range>
                <ml:real>0</ml:real>
                <ml:apply>
                  <ml:minus />
                  <ml:apply>
                    <ml:id>rows</ml:id>
                    <ml:id>basis</ml:id>
                  </ml:apply>
                  <ml:real>1</ml:real>
                </ml:apply>
              </ml:range>
              <ml:program>
                <ml:localDefine>
                  <ml:id>j</ml:id>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>basis</ml:id>
                    <ml:sequence>
                      <ml:id>r</ml:id>
                      <ml:real>0</ml:real>
                    </ml:sequence>
                  </ml:apply>
                </ml:localDefine>
                <ml:localDefine>
                  <ml:id>b</ml:id>
                  <ml:apply>
                    <ml:indexer />
                    <ml:id>basis</ml:id>
                    <ml:sequence>
                      <ml:id>r</ml:id>
                      <ml:real>1</ml:real>
                    </ml:sequence>
                  </ml:apply>
                </ml:localDefine>
                <ml:localDefine>
                  <ml:id>ttj</ml:id>
                  <ml:apply>
                    <ml:pow />
                    <ml:real>2</ml:real>
                    <ml:id>j</ml:id>
                  </ml:apply>
                </ml:localDefine>
                <ml:localDefine>
                  <ml:id>packet</ml:id>
                  <ml:apply>
                    <ml:id>get_subband</ml:id>
                    <ml:sequence>
                      <ml:id>w</ml:id>
                      <ml:id>j</ml:id>
                      <ml:id>b</ml:id>
                    </ml:sequence>
                  </ml:apply>
                </ml:localDefine>
                <ml:for>
                  <ml:id>k</ml:id>
                  <ml:range>
                    <ml:real>0</ml:real>
                    <ml:apply>
                      <ml:minus />
                      <ml:apply>
                        <ml:div />
                        <ml:id>N</ml:id>
                        <ml:id>ttj</ml:id>
                      </ml:apply>
                      <ml:real>1</ml:real>
                    </ml:apply>
                  </ml:range>
                  <ml:program>
                    <ml:localDefine>
                      <ml:id>coeff</ml:id>
                      <ml:apply>
                        <ml:indexer />
                        <ml:id>packet</ml:id>
                        <ml:id>k</ml:id>
                      </ml:apply>
                    </ml:localDefine>
                    <ml:for>
                      <ml:id>x</ml:id>
                      <ml:range>
                        <ml:apply>
                          <ml:mult style="default" />
                          <ml:apply>
                            <ml:mult style="default" />
                            <ml:id>hsize</ml:id>
                            <ml:id>ttj</ml:id>
                          </ml:apply>
                          <ml:id>k</ml:id>
                        </ml:apply>
                        <ml:apply>
                          <ml:minus />
                          <ml:apply>
                            <ml:mult style="default" />
                            <ml:apply>
                              <ml:mult style="default" />
                              <ml:id>hsize</ml:id>
                              <ml:id>ttj</ml:id>
                            </ml:apply>
                            <ml:parens>
                              <ml:apply>
                                <ml:plus />
                                <ml:id>k</ml:id>
                                <ml:real>1</ml:real>
                              </ml:apply>
                            </ml:parens>
                          </ml:apply>
                          <ml:real>1</ml:real>
                        </ml:apply>
                      </ml:range>
                      <ml:for>
                        <ml:id>y</ml:id>
                        <ml:range>
                          <ml:apply>
                            <ml:mult style="default" />
                            <ml:apply>
                              <ml:mult style="default" />
                              <ml:id>vsize</ml:id>
                              <ml:id>N</ml:id>
                            </ml:apply>
                            <ml:apply>
                              <ml:div />
                              <ml:id>b</ml:id>
                              <ml:id>ttj</ml:id>
                            </ml:apply>
                          </ml:apply>
                          <ml:apply>
                            <ml:minus />
                            <ml:apply>
                              <ml:mult style="default" />
                              <ml:apply>
                                <ml:mult style="default" />
                                <ml:id>vsize</ml:id>
                                <ml:id>N</ml:id>
                              </ml:apply>
                              <ml:apply>
                                <ml:div />
                                <ml:apply>
                                  <ml:plus />
                                  <ml:id>b</ml:id>
                                  <ml:real>1</ml:real>
                                </ml:apply>
                                <ml:id>ttj</ml:id>
                              </ml:apply>
                            </ml:apply>
                            <ml:real>1</ml:real>
                          </ml:apply>
                        </ml:range>
                        <ml:localDefine>
                          <ml:apply>
                            <ml:indexer />
                            <ml:id>Q</ml:id>
                            <ml:sequence>
                              <ml:apply>
                                <ml:minus />
                                <ml:apply>
                                  <ml:minus />
                                  <ml:id>vextent</ml:id>
                                  <ml:real>1</ml:real>
                                </ml:apply>
                                <ml:id>y</ml:id>
                              </ml:apply>
                              <ml:id>x</ml:id>
                            </ml:sequence>
                          </ml:apply>
                          <ml:apply>
                            <ml:absval />
                            <ml:id>coeff</ml:id>
                          </ml:apply>
                        </ml:localDefine>
                      </ml:for>
                    </ml:for>
                  </ml:program>
                </ml:for>
              </ml:program>
            </ml:for>
            <ml:apply>
              <ml:minus />
              <ml:real font="0">255</ml:real>
              <ml:apply>
                <ml:id>scale</ml:id>
                <ml:id>Q</ml:id>
              </ml:apply>
            </ml:apply>
          </ml:program>
        </ml:define>
      </math>
      <indexes>
        <phrase>tfPlotFromWPT function</phrase>
      </indexes>
      <rendering item-idref="26" />
    </region>
    <region region-id="4620" left="0" top="4242" width="6000" height="6" align-x="0" align-y="4242" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="">
      <pageBreak />
    </region>
    <region region-id="4928" left="6" top="4254.75" width="322.5" height="28.5" align-x="6" align-y="4266" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Heading 1" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Tapers that can be used with the Local Cosine Transforms lct(a,n,f) and ilct(w,n,b,f).</p>
      </text>
      <indexes>
        <phrase>cosine transforms, tapers for local</phrase>
        <phrase>tapers for local cosine transforms</phrase>
      </indexes>
    </region>
    <region region-id="4948" left="6" top="4292.25" width="73.5" height="27.75" align-x="37.5" align-y="4308" show-border="false" show-highlight="false" is-protected="true" background-color="#ff8000" tag="">
      <math optimize="false" export="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id>box</ml:id>
            <ml:boundVars>
              <ml:id>x</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:parens>
            <ml:apply>
              <ml:greaterThan />
              <ml:id>x</ml:id>
              <ml:apply>
                <ml:div />
                <ml:real>1</ml:real>
                <ml:real>2</ml:real>
              </ml:apply>
            </ml:apply>
          </ml:parens>
        </ml:define>
      </math>
      <indexes>
        <phrase>box taper</phrase>
      </indexes>
      <rendering item-idref="27" />
    </region>
    <region region-id="4930" left="6" top="4339.5" width="57.75" height="14.25" align-x="45.75" align-y="4350" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="">
      <math optimize="false" export="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id>poly1</ml:id>
            <ml:boundVars>
              <ml:id>x</ml:id>
            </ml:boundVars>
          </ml:function>
          <ml:apply>
            <ml:sqrt />
            <ml:id>x</ml:id>
          </ml:apply>
        </ml:define>
      </math>
      <indexes>
        <phrase>poly1 taper</phrase>
      </indexes>
      <rendering item-idref="28" />
    </region>
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      <math optimize="false" export="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id>poly2</ml:id>
            <ml:boundVars>
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          <ml:apply>
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            <ml:apply>
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              <ml:apply>
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                <ml:apply>
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        <phrase>poly2 taper</phrase>
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        <ml:define>
          <ml:function>
            <ml:id>poly3</ml:id>
            <ml:boundVars>
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          <ml:apply>
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            <ml:apply>
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              <ml:apply>
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                <ml:apply>
                  <ml:mult style="default" />
                  <ml:real>10</ml:real>
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                </ml:apply>
                <ml:apply>
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                  <ml:real>15</ml:real>
                  <ml:apply>
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                    <ml:real>4</ml:real>
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                </ml:apply>
              </ml:apply>
              <ml:apply>
                <ml:mult style="default" />
                <ml:real>6</ml:real>
                <ml:apply>
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                  <ml:real>5</ml:real>
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              </ml:apply>
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      <indexes>
        <phrase>poly3 taper</phrase>
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      <math optimize="false" export="false" disable-calc="false">
        <ml:define>
          <ml:function>
            <ml:id>poly4</ml:id>
            <ml:boundVars>
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            </ml:boundVars>
          </ml:function>
          <ml:apply>
            <ml:mult style="default" />
            <ml:apply>
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            <ml:apply>
              <ml:sqrt />
              <ml:apply>
                <ml:minus />
                <ml:apply>
                  <ml:plus />
                  <ml:apply>
                    <ml:minus />
                    <ml:real>35</ml:real>
                    <ml:apply>
                      <ml:mult style="default" />
                      <ml:real>84</ml:real>
                      <ml:id>x</ml:id>
                    </ml:apply>
                  </ml:apply>
                  <ml:apply>
                    <ml:mult style="default" />
                    <ml:real>70</ml:real>
                    <ml:apply>
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                      <ml:real>2</ml:real>
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                  </ml:apply>
                </ml:apply>
                <ml:apply>
                  <ml:mult style="default" />
                  <ml:real>20</ml:real>
                  <ml:apply>
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                    <ml:id>x</ml:id>
                    <ml:real>3</ml:real>
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      <math optimize="false" export="false" disable-calc="false">
        <ml:define>
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            <ml:boundVars>
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            <ml:apply>
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              <ml:apply>
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