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                <c val="#008080">SECTION 4 - DIGITAL FILTERING</c>
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        <phrase>filtering, digital</phrase>
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        <phrase>lowpass function</phrase>
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        <phrase>bandpass function</phrase>
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        <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">These functions use windowing of the impulse response of an ideal filter to generate coefficients for an FIR filter of the given type. </p>
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        <phrase>filter, ideal, windowing of impulse response of an</phrase>
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          <b>f</b>, <b>f</b><b><sub>1</sub></b>, <b>f</b><b><sub>2</sub></b>, real-valued cutoff or bandpass frequencies, given as fraction of the sampling frequency, between 0 and 0.5</p>
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              <b>N</b>
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          </inlineAttr>, integer &gt;2 number of coefficients for the filter</p>
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          </f>, (optional) windowing function index. Rectangular window if unspecified. </p>
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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">4</p>
        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">5</p>
        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">6 </p>
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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">rectangular (the default)</p>
        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">tapered rectangular</p>
        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">triangular</p>
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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">Blackman</p>
        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Nuttall</p>
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        <phrase>window, Blackman</phrase>
        <phrase>window, Hamming</phrase>
        <phrase>window, Hanning</phrase>
        <phrase>Blackman window</phrase>
        <phrase>Hamming window</phrase>
        <phrase>Hanning window</phrase>
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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">Return an N-element vector containing the filter coefficients.</p>
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            </b>
          </f>For definitions and plots of available windows, see the section on <b><u><link href="./Windows.xmcd" title="Links to section" popup="false">Signal Windowing</link></u></b>. </p>
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          </f>If the window type is not specified, the functions use the current default as set by the function <b>setwindow</b>. However, note that this function is now deprecated and future versions of the Extension Pack may not support it. To ensure compatibility with the future versions, do not use <b>setwindow</b> to change the default window type.</p>
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        <phrase>signal windowing</phrase>
        <phrase>windowing, signal</phrase>
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        <phrase>lowpass filter window comparison</phrase>
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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">Calculate coefficients for a lowpass filter using two different windows, rectangular and Blackman. The normalized cutoff frequency is .2</p>
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        <phrase>window, Blackman</phrase>
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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">Set the cutoff frequency and number of coefficients.</p>
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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">Calculate the coefficients with rectangular and Blackman windows.</p>
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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">Define a range for displaying the coefficients and computing the frequency response.</p>
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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">The coefficients:</p>
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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">Now we calculate the phase and magnitude of the frequency responses. See the <b><u><link href="./Funcs.xmcd" title="Links to section" popup="false">Elementwise magnitude and phase</link></u></b> section for a discussion of <f family="Times New Roman" charset="0"><b><inlineAttr line-through="false">mag</inlineAttr></b></f><f family="Times New Roman" charset="0" size="12">, </f><f family="Times New Roman" charset="0"><b><inlineAttr line-through="false">phase</inlineAttr></b></f>, and <f family="Times New Roman" charset="0"><b><inlineAttr line-through="false">phasecor</inlineAttr></b></f><f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">. </inlineAttr></f>See the<f family="Arial" charset="0"><sp /></f><u><b><link href="./Gain.xmcd" title="Links to section" popup="false">Filter Gain</link></b></u> section for the<b><sp /></b><b>gain</b> function and the <b><u><link href="./Response.xmcd" title="Links to section" popup="false">Filter Response</link></u></b> section for more details on computing the <f family="Times New Roman" charset="0"><b><inlineAttr line-through="false">response</inlineAttr></b></f> function.</p>
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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">Magnitude:</p>
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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">Plots of magnitude, dB magnitude and phase of frequency response:</p>
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                <c val="#800000">Example - Filtering by Convolution</c>
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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">Convolution can be used to apply these FIR coefficients. Consider a signal with low, middle, and high frequencies normalized with respect to the sampling frequency.</p>
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      <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">Now we generate filter coefficients using a Hamming window (number 5):</p>
      </text>
      <indexes>
        <phrase>Hamming window</phrase>
      </indexes>
    </region>
    <region region-id="249" left="6" top="2046.75" width="324.75" height="14.25" align-x="6" align-y="2058" 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">Normalized filter cutoff frequencies are used to generate the coefficients.</p>
      </text>
    </region>
    <region region-id="252" left="36" top="2070.75" width="57" height="18" align-x="61.5" align-y="2082" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag="">
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      <rendering item-idref="35" />
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      <math optimize="false" disable-calc="false">
        <ml:define>
          <ml:id xml:space="preserve" subscript="high">f</ml:id>
          <ml:real>0.075</ml:real>
        </ml:define>
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      <rendering item-idref="36" />
    </region>
    <region region-id="421" left="222" top="2070.75" width="33" height="15.75" align-x="238.5" align-y="2082" show-border="false" show-highlight="true" 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:real>5</ml:real>
        </ml:define>
      </math>
      <rendering item-idref="37" />
    </region>
    <region region-id="55" left="36" top="2100.75" width="123" height="18" align-x="51" align-y="2112" 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="WarnRedefinedBIUnit">
          <ml:id xml:space="preserve">L</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">lowpass</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve" subscript="low">f</ml:id>
              <ml:real>51</ml:real>
              <ml:id xml:space="preserve">w</ml:id>
            </ml:sequence>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="38" />
    </region>
    <region region-id="56" left="36" top="2124.75" width="129.75" height="18" align-x="52.5" align-y="2136" 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="WarnRedefinedBIUnit">
          <ml:id xml:space="preserve">H</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">highpass</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve" subscript="high">f</ml:id>
              <ml:real>51</ml:real>
              <ml:id xml:space="preserve">w</ml:id>
            </ml:sequence>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="39" />
    </region>
    <region region-id="57" left="36" top="2148.75" width="155.25" height="18" align-x="51" align-y="2160" 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="WarnRedefinedBIUnit">
          <ml:id xml:space="preserve">S</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">bandstop</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve" subscript="low">f</ml:id>
              <ml:id xml:space="preserve" subscript="high">f</ml:id>
              <ml:real>51</ml:real>
              <ml:id xml:space="preserve">w</ml:id>
            </ml:sequence>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="40" />
    </region>
    <region region-id="58" left="36" top="2172.75" width="156" height="18" align-x="51" align-y="2184" 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">P</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">bandpass</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve" subscript="low">f</ml:id>
              <ml:id xml:space="preserve" subscript="high">f</ml:id>
              <ml:real>51</ml:real>
              <ml:id xml:space="preserve">w</ml:id>
            </ml:sequence>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="41" />
    </region>
    <region region-id="217" left="6" top="2202.75" width="298.5" height="57" align-x="6" align-y="2214" 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">To filter the signal, convolve the filter impulse responses with <f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">x</inlineAttr></f> using <f family="Times New Roman" charset="0"><b><inlineAttr line-through="false">convol</inlineAttr></b></f> for the first two and <f family="Times New Roman" charset="0"><b><inlineAttr line-through="false">response</inlineAttr></b></f> for the second two, demonstrating two approaches to this task. See <b><u><link href="./Response.xmcd" title="Links to section" popup="false">Filter Response</link></u></b> for a discussion of <f family="Times New Roman" charset="0"><b><inlineAttr line-through="false">response</inlineAttr></b></f> function). </p>
      </text>
      <indexes>
        <phrase>filter response</phrase>
        <phrase>response function</phrase>
        <phrase>function, response</phrase>
      </indexes>
    </region>
    <region region-id="164" left="36" top="2268.75" width="97.5" height="15.75" align-x="65.25" align-y="2280" 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">Lout</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">convol</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">x</ml:id>
              <ml:id xml:space="preserve">L</ml:id>
            </ml:sequence>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="42" />
    </region>
    <region region-id="165" left="192" top="2268.75" width="100.5" height="15.75" align-x="222.75" align-y="2280" 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">Hout</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">convol</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">x</ml:id>
              <ml:id xml:space="preserve">H</ml:id>
            </ml:sequence>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="43" />
    </region>
    <region region-id="166" left="36" top="2292.75" width="123" height="15.75" align-x="65.25" align-y="2304" 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">Sout</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">response</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">x</ml:id>
              <ml:id xml:space="preserve">S</ml:id>
              <ml:id xml:space="preserve">N</ml:id>
            </ml:sequence>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="44" />
    </region>
    <region region-id="167" left="192" top="2292.75" width="123" height="15.75" align-x="221.25" align-y="2304" 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">Pout</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">response</ml:id>
            <ml:sequence>
              <ml:id xml:space="preserve">x</ml:id>
              <ml:id xml:space="preserve">P</ml:id>
              <ml:id xml:space="preserve">N</ml:id>
            </ml:sequence>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="45" />
    </region>
    <region region-id="169" left="6" top="2316.75" width="315.75" height="57" align-x="6" align-y="2328" 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">The outputs of <f family="Times New Roman" charset="0"><b><inlineAttr line-through="false">convol</inlineAttr></b></f> have length equal to one less than the sum of the lengths of <f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">x</inlineAttr></f> and the coefficient array. For more on the convolution and correlation functions see <b><u><link href="./Conv.xmcd" title="Links to section" popup="false">Convolution and Correlation</link></u></b> in Section 1. </p>
      </text>
      <indexes>
        <phrase>convol function</phrase>
        <phrase>function, convol</phrase>
        <phrase>convolution and correlation</phrase>
        <phrase>correlation and convolution</phrase>
      </indexes>
    </region>
    <region region-id="170" left="6" top="2382.75" width="119.25" height="14.25" align-x="6" align-y="2394" 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">Define a range for plotting:</p>
      </text>
    </region>
    <region region-id="463" left="36" top="2400.75" width="115.5" height="15.75" align-x="49.5" align-y="2412" 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">n</ml:id>
          <ml:range>
            <ml:real>0</ml:real>
            <ml:apply>
              <ml:minus />
              <ml:apply>
                <ml:id xml:space="preserve">length</ml:id>
                <ml:id xml:space="preserve">Lout</ml:id>
              </ml:apply>
              <ml:real>1</ml:real>
            </ml:apply>
          </ml:range>
        </ml:define>
      </math>
      <rendering item-idref="46" />
    </region>
    <region region-id="277" left="0" top="2430" width="6000" height="6" align-x="0" align-y="2430" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <pageBreak />
    </region>
    <region region-id="422" left="6" top="2442.75" width="324" height="57" align-x="6" align-y="2454" 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">Examine the lowpass output. Just the low frequency component of the signal is plotted in blue for comparison. The sine wave is shifted to the right by 25 to allow for the delay introduced by the filter. The filter passes essentially only the low frequency, with some attenuation.</p>
      </text>
    </region>
    <region region-id="423" left="24" top="2508" width="348.75" height="139.5" align-x="24" align-y="2508" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <plot disable-calc="false" item-idref="47" />
      <rendering item-idref="48" />
    </region>
    <region region-id="180" left="6" top="2652.75" width="292.5" height="42.75" align-x="6" align-y="2664" 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">Examine the effectiveness of the bandpass filter by comparing the spectrum of the original signal with the spectrum after filtering. Only the first 80 spectrum values are shown.</p>
      </text>
    </region>
    <region region-id="432" left="36" top="2706.75" width="66" height="15.75" align-x="48" align-y="2718" 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:apply>
            <ml:id xml:space="preserve">CFFT</ml:id>
            <ml:id xml:space="preserve">x</ml:id>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="49" />
    </region>
    <region region-id="433" left="132" top="2706.75" width="87" height="15.75" align-x="149.25" align-y="2718" 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">O</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">CFFT</ml:id>
            <ml:id xml:space="preserve">Pout</ml:id>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="50" />
    </region>
    <region region-id="436" left="18" top="2736" width="182.25" height="115.5" align-x="18" align-y="2736" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <plot disable-calc="false" item-idref="51" />
      <rendering item-idref="52" />
    </region>
    <region region-id="437" left="222" top="2736" width="182.25" height="115.5" align-x="222" align-y="2736" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <plot disable-calc="false" item-idref="53" />
      <rendering item-idref="54" />
    </region>
    <region region-id="438" left="6" top="2862.75" width="318.75" height="28.5" align-x="6" align-y="2874" 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">Most of the low frequency and all of the high frequency have been successfully attenuated.</p>
      </text>
    </region>
    <region region-id="78" left="0" top="2898" width="6000" height="6" align-x="0" align-y="2898" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <pageBreak />
    </region>
    <region region-id="184" left="6" top="2910.75" width="321" height="42.75" align-x="6" align-y="2922" 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">This plot compares the highpass output with the high frequency signal component. Although the output of the filter is delayed by the expected 25 samples, the frequencies are the same.</p>
      </text>
    </region>
    <region region-id="439" left="24" top="2958" width="305.25" height="139.5" align-x="24" align-y="2958" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <plot disable-calc="false" item-idref="55" />
      <rendering item-idref="56" />
    </region>
    <region region-id="188" left="6" top="3108.75" width="322.5" height="42.75" align-x="6" align-y="3120" 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">Finally, we compare the spectrum of the original signal with the spectrum of the output of the bandstop filter <f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">S, showing the attenuation of the central frequency.</inlineAttr></f></p>
      </text>
      <indexes>
        <phrase>bandstop filter</phrase>
        <phrase>filter, bandstop</phrase>
      </indexes>
    </region>
    <region region-id="449" left="36" top="3156.75" width="66" height="15.75" align-x="48" align-y="3168" 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">I</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">CFFT</ml:id>
            <ml:id xml:space="preserve">x</ml:id>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="57" />
    </region>
    <region region-id="450" left="150" top="3156.75" width="87" height="15.75" align-x="167.25" align-y="3168" 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">O</ml:id>
          <ml:apply>
            <ml:id xml:space="preserve">CFFT</ml:id>
            <ml:id xml:space="preserve">Sout</ml:id>
          </ml:apply>
        </ml:define>
      </math>
      <rendering item-idref="58" />
    </region>
    <region region-id="446" left="18" top="3180" width="170.25" height="115.5" align-x="18" align-y="3180" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <plot disable-calc="false" item-idref="59" />
      <rendering item-idref="60" />
    </region>
    <region region-id="448" left="204" top="3180" width="170.25" height="115.5" align-x="204" align-y="3180" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <plot disable-calc="false" item-idref="61" />
      <rendering item-idref="62" />
    </region>
    <region region-id="300" left="0" top="3324" width="6000" height="6" align-x="0" align-y="3324" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <pageBreak />
    </region>
    <region region-id="451" left="6" top="3336.75" width="162.75" height="14.25" align-x="6" align-y="3348" 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">
          <f family="Times New Roman" charset="0">
            <b>
              <inlineAttr font-style="normal" line-through="false">
                <c val="#800000">setwindow(w) - DEPRECATED</c>
              </inlineAttr>
            </b>
          </f>
        </p>
      </text>
      <indexes>
        <phrase>setwindow function, deprecated</phrase>
        <phrase>deprecated setwindow function</phrase>
        <phrase>function, setwindow, deprecated</phrase>
      </indexes>
    </region>
    <region region-id="453" left="6" top="3360.75" width="297.75" height="171" align-x="6" align-y="3372" 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">This function lets you change the value of the default window used to design FIR filters. It is now DEPRECATED, and you should avoid using it. Instead, if you want to use windows other than the rectangular one when designing FIR filters, specify the window type as an optional argument into the FIR filter design</p>
        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">function. </p>
        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit" />
        <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">When a new document is opened, the default window is rectangular (window number 1). To use a Hamming window, use <f family="Times New Roman" charset="0"><b><inlineAttr line-through="false">setwindow</inlineAttr></b></f><f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">(5)</inlineAttr></f><f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">.</inlineAttr></f> To make the setting take effect, you must actually calculate the function by typing an equals sign. <f family="Times New Roman" charset="0"><inlineAttr font-weight="normal" line-through="false">Mathcad</inlineAttr></f> confirms the setting by showing the new value.</p>
      </text>
      <indexes>
        <phrase>Hamming window</phrase>
        <phrase>FIR filters</phrase>
        <phrase>filters, FIR</phrase>
      </indexes>
    </region>
    <region region-id="460" left="36" top="3540.75" width="93.75" height="15.75" align-x="108" align-y="3552" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
      <math optimize="false" disable-calc="false">
        <ml:eval>
          <ml:apply>
            <ml:id xml:space="preserve">setwindow</ml:id>
            <ml:real>5</ml:real>
          </ml:apply>
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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">To find out what the current window is, use an argument of <f family="MS Serif" charset="0"><inlineAttr font-weight="normal" line-through="false">0</inlineAttr></f>:</p>
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        <ml:eval>
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