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        <p style="Chapter Head" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">WAVELETS EXTENSION PACK</p>
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              <c val="#000"> with the contents of the vector </c>
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              <c val="#000">. The arguments to these functions are:</c>
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          <c val="#000"> the one-dimensional (1D) wavelet packet transform coefficients.</c>
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          <c val="#000"> the two-dimensional (2D) wavelet packet transform coefficients.</c>
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          <c val="#000"> the level of the desired block/subband of coefficients.</c>
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          <c val="#000"> the index of the desired block/subband of coefficients.</c>
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          <c val="#000"> the vector of new values for the coefficients in the block/subband.</c>
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          <c val="#000"> the matrix of new values for the coefficients in the block/subband.</c>
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    <region region-id="11" left="0" top="426" width="6000" height="6" align-x="0" align-y="426" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <pageBreak />
    </region>
    <region region-id="4475" left="6" top="438.75" width="108.75" height="14.25" align-x="6" align-y="450" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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">1D Subband Insertion</p>
      </text>
      <indexes>
        <phrase>1D subband insertion</phrase>
      </indexes>
    </region>
    <region region-id="4572" left="30" top="462.75" width="111" height="14.25" align-x="30" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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">
          <f family="Times New Roman" charset="0" size="12">
            <b>
              <inlineAttr line-through="false">
                <c val="#000">put_subband(w, l, n, y)</c>
              </inlineAttr>
            </b>
          </f>
        </p>
      </text>
      <indexes>
        <phrase>put_subband function</phrase>
      </indexes>
    </region>
    <region region-id="4573" left="30" top="486.75" width="93.75" height="14.25" align-x="30" align-y="498" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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">
          <f family="Times New Roman" charset="0" size="12">
            <b>
              <inlineAttr line-through="false">
                <c val="#000">put_smooth(w, l, y)</c>
              </inlineAttr>
            </b>
          </f>
        </p>
      </text>
      <indexes>
        <phrase>put_smooth function</phrase>
      </indexes>
    </region>
    <region region-id="4574" left="30" top="510.75" width="85.5" height="14.25" align-x="30" align-y="522" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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">
          <f family="Times New Roman" charset="0" size="12">
            <b>
              <inlineAttr line-through="false">
                <c val="#000">put_detail(w, l, y)</c>
              </inlineAttr>
            </b>
          </f>
        </p>
      </text>
      <indexes>
        <phrase>put_detail function</phrase>
      </indexes>
    </region>
    <region region-id="4581" left="6" top="540.75" width="323.25" height="102.75" align-x="6" align-y="552" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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="0" text-align="left" list-style-type="none" tabs="inherit">
          <inlineAttr font-weight="normal">
            <c val="#000">The function </c>
          </inlineAttr>
          <f family="Times New Roman" charset="0">
            <b>
              <inlineAttr line-through="false">
                <c val="#000">put_subband</c>
              </inlineAttr>
            </b>
          </f>
          <inlineAttr font-weight="normal">
            <c val="#000"> replaces the block of coefficients in</c>
          </inlineAttr>
          <f family="Times New Roman" charset="0">
            <c val="#000">
              <inlineAttr font-weight="normal" line-through="false">
                <sp />
              </inlineAttr>
            </c>
          </f>
          <f family="Times New Roman" charset="0">
            <b>
              <inlineAttr line-through="false">
                <c val="#000">w</c>
              </inlineAttr>
            </b>
          </f>
          <f family="Times New Roman" charset="0">
            <inlineAttr font-weight="normal" line-through="false">
              <c val="#000"> corresponding to the </c>
            </inlineAttr>
          </f>
          <f family="Times New Roman" charset="0">
            <c val="#000">
              <b>
                <inlineAttr line-through="false">n</inlineAttr>
              </b>
            </c>
          </f>
          <f family="Times New Roman" charset="0" size="12">
            <inlineAttr font-weight="normal" line-through="false">
              <c val="#000">
                <sup>th</sup>
              </c>
            </inlineAttr>
          </f>
          <f family="Times New Roman" charset="0">
            <inlineAttr font-weight="normal" line-through="false">
              <c val="#000"> wavelet packet at level </c>
            </inlineAttr>
          </f>
          <f family="Times New Roman" charset="0">
            <inlineAttr line-through="false">
              <c val="#000">
                <b>l</b>
              </c>
            </inlineAttr>
          </f>
          <inlineAttr font-weight="normal" line-through="false">
            <f family="Times New Roman" charset="0">
              <c val="#000"> by the data in </c>
            </f>
          </inlineAttr>
          <f family="Times New Roman" charset="0">
            <b>
              <inlineAttr line-through="false">
                <c val="#000">y</c>
              </inlineAttr>
            </b>
          </f>
          <f family="Times New Roman" charset="0">
            <inlineAttr font-weight="normal" line-through="false">
              <c val="#000">. Note that the size of </c>
            </inlineAttr>
          </f>
          <f family="Times New Roman" charset="0">
            <b>
              <inlineAttr line-through="false">
                <c val="#000">y</c>
              </inlineAttr>
            </b>
          </f>
          <f family="Times New Roman" charset="0">
            <inlineAttr font-weight="normal" line-through="false">
              <c val="#000"> must be the same as that of the subband it is to replac</c>
            </inlineAttr>
          </f>
          <inlineAttr font-weight="normal">
            <c val="#000">e. The shortcut versions of </c>
          </inlineAttr>
          <f family="Times New Roman" charset="0">
            <b>
              <inlineAttr line-through="false">
                <c val="#000">put_subband</c>
              </inlineAttr>
            </b>
          </f>
          <inlineAttr font-weight="normal">
            <c val="#000"> allow a more intuitive approach. </c>
          </inlineAttr>
          <f family="Times New Roman" charset="0">
            <b>
              <inlineAttr line-through="false">
                <c val="#000">put_smooth</c>
              </inlineAttr>
            </b>
          </f>
          <c val="#000">
            <inlineAttr font-weight="normal"> replaces the contents of the father coefficients with the contents of </inlineAttr>
          </c>
          <f family="Times New Roman" charset="0">
            <b>
              <inlineAttr line-through="false">
                <c val="#000">y</c>
              </inlineAttr>
            </b>
          </f>
          <f family="Times New Roman" charset="0">
            <inlineAttr font-weight="normal" line-through="false">
              <c val="#000">. </c>
            </inlineAttr>
          </f>
          <inlineAttr font-weight="normal">
            <c val="#000">Similarly, </c>
          </inlineAttr>
          <c val="#000">
            <b>put_detail</b>
          </c>
          <c val="#000"> replaces the contents of the mother coefficients with the contents of </c>
          <b>
            <c val="#000">y</c>
          </b>
          <c val="#000">. For</c>
          <inlineAttr font-weight="normal">
            <c val="#000"> example:</c>
          </inlineAttr>
        </p>
      </text>
    </region>
    <region region-id="4412" left="30" top="648.75" width="149.25" height="15.75" align-x="43.5" align-y="660" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:id xml:space="preserve">v</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">READPRN</ml:id>
            <ml:str xml:space="preserve">wavelet.prn</ml:str>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="6" />
    </region>
    <region region-id="4422" left="198" top="648.75" width="87" height="14.25" align-x="198" align-y="660" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Read in some data.</p>
      </text>
    </region>
    <region region-id="4425" left="198" top="672.75" width="141.75" height="28.5" align-x="198" align-y="684" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Perform a symmetric DWT on the data.</p>
      </text>
    </region>
    <region region-id="4413" left="30" top="678.75" width="142.5" height="15.75" align-x="46.5" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:id xml:space="preserve">w</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">dwts</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">v</ml:id>
              <ml:real>4</ml:real>
              <ml:apply>
                <ml:id xml:space="preserve">Bspline</ml:id>
                <ml:sequence>
                  <ml:real>3</ml:real>
                  <ml:real>3</ml:real>
                </ml:sequence>
              </ml:apply>
            </ml:sequence>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="7" />
    </region>
    <region region-id="4414" left="30" top="708.75" width="129" height="15.75" align-x="48.75" align-y="720" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:id xml:space="preserve">sb</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">get_subband</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">w</ml:id>
              <ml:real>4</ml:real>
              <ml:real>0</ml:real>
            </ml:sequence>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="8" />
    </region>
    <region region-id="4418" left="198" top="708.75" width="143.25" height="28.5" align-x="198" align-y="720" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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="0" text-align="left" list-style-type="none" tabs="inherit">Extract the subband of the father wavelet coefficients.</p>
      </text>
    </region>
    <region region-id="4493" left="30" top="750.75" width="116.25" height="15.75" align-x="53.25" align-y="762" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:id xml:space="preserve">sbf</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">get_smooth</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">w</ml:id>
              <ml:real>4</ml:real>
            </ml:sequence>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="9" />
    </region>
    <region region-id="4496" left="198" top="750.75" width="145.5" height="57" align-x="198" align-y="762" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Remember that <f family="Times New Roman" charset="0"><b><inlineAttr line-through="false">get_smooth</inlineAttr></b></f>, a shortcut version of <f family="Times New Roman" charset="0"><b><inlineAttr line-through="false">get_subband</inlineAttr></b></f><f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">,</inlineAttr></f> provides the same results.</p>
      </text>
    </region>
    <region region-id="4415" left="30" top="816.75" width="153.75" height="15.75" align-x="46.5" align-y="828" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedUDScalar">
          <ml:id xml:space="preserve">w</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">put_subband</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">w</ml:id>
              <ml:real>4</ml:real>
              <ml:real>0</ml:real>
              <ml:apply>
                <ml:mult style="default" />
                <ml:id xml:space="preserve">sb</ml:id>
                <ml:real>0</ml:real>
              </ml:apply>
            </ml:sequence>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="10" />
    </region>
    <region region-id="4404" left="198" top="816.75" width="132.75" height="28.5" align-x="198" align-y="828" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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="0" text-align="left" list-style-type="none" tabs="inherit">Replace the coefficients in the father subband by 0.</p>
      </text>
    </region>
    <region region-id="4505" left="30" top="858.75" width="141" height="15.75" align-x="51" align-y="870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:id xml:space="preserve">wf</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">put_smooth</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">w</ml:id>
              <ml:real>4</ml:real>
              <ml:apply>
                <ml:mult style="default" />
                <ml:id xml:space="preserve">sb</ml:id>
                <ml:real>0</ml:real>
              </ml:apply>
            </ml:sequence>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="11" />
    </region>
    <region region-id="4504" left="198" top="858.75" width="153.75" height="42.75" align-x="198" align-y="870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Or equivalently, use <f family="Times New Roman" charset="0"><b><inlineAttr line-through="false">put_smooth</inlineAttr></b></f>, the shortcut version of <f family="Times New Roman" charset="0"><b><inlineAttr line-through="false">put_subband</inlineAttr></b></f><f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">.</inlineAttr></f></p>
      </text>
    </region>
    <region region-id="4506" left="0" top="912" width="6000" height="6" align-x="0" align-y="912" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <pageBreak />
    </region>
    <region region-id="4420" left="30" top="918.75" width="144.75" height="15.75" align-x="43.5" align-y="930" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:id xml:space="preserve">x</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">idwts</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">w</ml:id>
              <ml:real>4</ml:real>
              <ml:apply>
                <ml:id xml:space="preserve">Bspline</ml:id>
                <ml:sequence>
                  <ml:real>3</ml:real>
                  <ml:real>3</ml:real>
                </ml:sequence>
              </ml:apply>
            </ml:sequence>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="12" />
    </region>
    <region region-id="4426" left="198" top="918.75" width="152.25" height="28.5" align-x="198" align-y="930" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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="0" text-align="left" list-style-type="none" tabs="inherit">Reconstruct the signal by performing an inverse transform.</p>
      </text>
    </region>
    <region region-id="4417" left="30" top="942.75" width="66.75" height="15.75" align-x="40.5" align-y="954" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:id xml:space="preserve">i</ml:id>
          <ml:range>
            <ml:real>0</ml:real>
            <ml:apply>
              <ml:id xml:space="preserve">last</ml:id>
              <ml:id xml:space="preserve">v</ml:id>
            </ml:apply>
          </ml:range>
        </ml:define>
      </math>
      <rendering item-idref="13" />
    </region>
    <region region-id="4427" left="6" top="972" width="357" height="187.5" align-x="6" align-y="972" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <plot disable-calc="false" item-idref="14" />
      <rendering item-idref="15" />
    </region>
    <region region-id="4515" left="0" top="1158" width="6000" height="6" align-x="0" align-y="1158" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <pageBreak />
    </region>
    <region region-id="4508" left="6" top="1170.75" width="108.75" height="14.25" align-x="6" align-y="1182" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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 Subband Insertion</p>
      </text>
      <indexes>
        <phrase>2D subband insertion</phrase>
      </indexes>
    </region>
    <region region-id="4585" left="24" top="1194.75" width="154.5" height="14.25" align-x="24" align-y="1206" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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="0" text-align="left" list-style-type="none" tabs="inherit">
          <f family="Times New Roman" charset="0" size="12">
            <b>
              <inlineAttr line-through="false">
                <c val="#000">put_subband2d(M, l, m, n, N)</c>
              </inlineAttr>
            </b>
          </f>
        </p>
      </text>
      <indexes>
        <phrase>put_subband2d function</phrase>
      </indexes>
    </region>
    <region region-id="4586" left="24" top="1218.75" width="138" height="14.25" align-x="24" align-y="1230" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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="0" text-align="left" list-style-type="none" tabs="inherit">
          <f family="Times New Roman" charset="0" size="12">
            <b>
              <inlineAttr line-through="false">
                <c val="#000">put_smooth2d(M, l, N)</c>
              </inlineAttr>
            </b>
          </f>
        </p>
      </text>
      <indexes>
        <phrase>put_smooth2d function</phrase>
      </indexes>
    </region>
    <region region-id="4587" left="24" top="1242.75" width="132" height="14.25" align-x="24" align-y="1254" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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="0" text-align="left" list-style-type="none" tabs="inherit">
          <f family="Times New Roman" charset="0" size="12">
            <b>
              <inlineAttr line-through="false">
                <c val="#000">put_detail2d(M, l, N, ds)</c>
              </inlineAttr>
            </b>
          </f>
        </p>
      </text>
      <indexes>
        <phrase>put_detail2d function</phrase>
      </indexes>
    </region>
    <region region-id="4588" left="6" top="1272.75" width="319.5" height="131.25" align-x="6" align-y="1284" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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="0" text-align="left" list-style-type="none" tabs="inherit">
          <inlineAttr font-weight="normal">
            <c val="#000">The function </c>
          </inlineAttr>
          <f family="Times New Roman" charset="0">
            <b>
              <inlineAttr line-through="false">
                <c val="#000">put_subband2d </c>
              </inlineAttr>
            </b>
          </f>
          <inlineAttr font-weight="normal">
            <c val="#000">replaces the block of coefficients in </c>
          </inlineAttr>
          <f family="Times New Roman" charset="0">
            <b>
              <inlineAttr line-through="false">
                <c val="#000">M</c>
              </inlineAttr>
            </b>
          </f>
          <inlineAttr font-weight="normal">
            <c val="#000"> corresponding to the (</c>
          </inlineAttr>
          <f family="Times New Roman" charset="0">
            <c val="#000">
              <b>
                <inlineAttr line-through="false">m</inlineAttr>
              </b>
            </c>
          </f>
          <f family="Times New Roman" charset="0">
            <b>
              <inlineAttr line-through="false">
                <c val="#000">,n</c>
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          </f>
          <inlineAttr font-weight="normal">
            <c val="#000">)</c>
          </inlineAttr>
          <inlineAttr font-weight="normal" line-through="false">
            <c val="#000">
              <sup>
                <f family="Times New Roman" charset="0" size="12">th</f>
              </sup>
            </c>
          </inlineAttr>
          <c val="#000">
            <inlineAttr font-weight="normal"> wavelet packet at level </inlineAttr>
          </c>
          <f family="Times New Roman" charset="0">
            <b>
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                <c val="#000">l</c>
              </inlineAttr>
            </b>
          </f>
          <c val="#000">
            <inlineAttr font-weight="normal"> by the data in </inlineAttr>
          </c>
          <f family="Times New Roman" charset="0">
            <b>
              <inlineAttr line-through="false">
                <c val="#000">N</c>
              </inlineAttr>
            </b>
          </f>
          <inlineAttr font-weight="normal">
            <c val="#000">. Note that the size of </c>
          </inlineAttr>
          <f family="Times New Roman" charset="0">
            <b>
              <inlineAttr line-through="false">
                <c val="#000">N</c>
              </inlineAttr>
            </b>
          </f>
          <inlineAttr font-weight="normal">
            <c val="#000"> must be the same as that of the subband it is to replace. </c>
          </inlineAttr>As in the 1D subband insertion functions, there are shortcut versions of <f family="Times New Roman" charset="0"><b><inlineAttr line-through="false">pu</inlineAttr></b></f><b>t_subband2d</b>. The functions <b>put_smooth2d</b> and <b>put_detail2d</b> insert the contents of <f family="Times New Roman" charset="0"><b><inlineAttr line-through="false">N</inlineAttr></b></f> into, respectively, the father and mother subbands at level <b>l</b> of the 2D wavelet packet transform <b>M</b>. The string argument <b>ds</b> is set to "H," "V," or "D" to indicate the horizontal, vertical, or diagonal mother subbands, respectively. For example<inlineAttr font-weight="normal"><c val="#000">:</c></inlineAttr></p>
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            <ml:indexer />
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              <ml:real>64</ml:real>
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    <region region-id="4437" left="222" top="1428.75" width="95.25" height="14.25" align-x="222" align-y="1440" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Create a zero matrix.</p>
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    <region region-id="4438" left="222" top="1452.75" width="138.75" height="28.5" align-x="222" align-y="1464" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
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        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Get the mother/mother subband at level 3.</p>
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        <ml:define warning="WarnRedefinedBIUnit">
          <ml:id xml:space="preserve">N</ml:id>
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            <ml:id xml:space="preserve">get_subband2d</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">M</ml:id>
              <ml:real>3</ml:real>
              <ml:real>0</ml:real>
              <ml:real>0</ml:real>
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    </region>
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      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedUDScalar">
          <ml:id xml:space="preserve">i</ml:id>
          <ml:range>
            <ml:real>0</ml:real>
            <ml:apply>
              <ml:minus />
              <ml:apply>
                <ml:id xml:space="preserve">rows</ml:id>
                <ml:id xml:space="preserve">N</ml:id>
              </ml:apply>
              <ml:real>1</ml:real>
            </ml:apply>
          </ml:range>
        </ml:define>
      </math>
      <rendering item-idref="18" />
    </region>
    <region region-id="4338" left="150" top="1494.75" width="93.75" height="15.75" align-x="162" align-y="1506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:id xml:space="preserve">j</ml:id>
          <ml:range>
            <ml:real>0</ml:real>
            <ml:apply>
              <ml:minus />
              <ml:apply>
                <ml:id xml:space="preserve">cols</ml:id>
                <ml:id xml:space="preserve">N</ml:id>
              </ml:apply>
              <ml:real>1</ml:real>
            </ml:apply>
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        </ml:define>
      </math>
      <rendering item-idref="19" />
    </region>
    <region region-id="4341" left="30" top="1524.75" width="69.75" height="17.25" align-x="58.5" align-y="1536" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:define warning="WarnRedefinedUDScalar">
          <ml:apply>
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              <ml:id xml:space="preserve">i</ml:id>
              <ml:id xml:space="preserve">j</ml:id>
            </ml:sequence>
          </ml:apply>
          <ml:apply>
            <ml:id xml:space="preserve">rnd</ml:id>
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        </ml:define>
      </math>
      <rendering item-idref="20" />
    </region>
    <region region-id="4440" left="222" top="1542.75" width="129" height="42.75" align-x="222" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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="0" text-align="left" list-style-type="none" tabs="inherit">Replace the subband with noise, then interpolate by inverse transforming.</p>
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      <math optimize="false" disable-calc="false">
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          <ml:id xml:space="preserve">M</ml:id>
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            <ml:id xml:space="preserve">put_subband2d</ml:id>
            <ml:sequence>
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              <ml:real>0</ml:real>
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                  <ml:real>9</ml:real>
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      <component hide-arguments="false" clsid-buddy="62e334b8-fdda-4b2b-9bb4-48def95f2af1" item-idref="23" disable-calc="false">
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        <outputs />
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      <rendering item-idref="24" />
    </region>
    <region region-id="4589" left="6" top="1902.75" width="315.75" height="57" align-x="6" align-y="1914" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <text use-page-width="false" push-down="false" lock-width="true">
        <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">An equivalent approach is to use the shortcut version of the function <f family="Times New Roman" charset="0"><b><inlineAttr line-through="false">put_subband2d</inlineAttr></b></f><f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">. Since the mother/mother subband was replaced, this corresponds to (m,n) = (0,0). This case corresponds to the smooth subband so we use the shortcut function </inlineAttr></f><b>put_smooth2d</b><f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">.</inlineAttr></f></p>
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      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:apply>
            <ml:indexer />
            <ml:id xml:space="preserve">M2</ml:id>
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              <ml:real>64</ml:real>
              <ml:real>64</ml:real>
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          </ml:apply>
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                  <ml:real>9</ml:real>
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      <pageBreak />
    </region>
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        <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Plot the inverse transform. The results are the same as above.</p>
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