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<p class="MsoNormal"><span style="font-size:14.0pt;line-height:107%;font-family:
"Arial",sans-serif">Digital filters are designed by either a direct method (e.g., least squares, Remez) or through the indirect use of an “analog prototype” (Impulse-Invariant,
Bilinear-Z-Transform).<span style="mso-spacerun:yes"> </span>In the case of an analog prototype, some desirable analog performance characteristic is preserved in the process.<span style="mso-spacerun:yes">
</span>With Bilinear-Z, it is the SHAPE of the frequency response that is preserved.
<span style="mso-spacerun:yes"> </span>It is classic (50 years) and terms such as “prototype”, “cutoff warping”, and “pre-warping” (Andy above) are always seen with BZT: </span></p>
<p class="MsoNormal"><span style="font-size:14.0pt;line-height:107%;font-family:
"Arial",sans-serif"> <span style="mso-spacerun:yes"> </span><o:p></o:p></span></p>
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</span><span style="mso-spacerun:yes"> </span><a href="http://electronotes.netfirms.com/EN197.pdf" id="LPlnk319587" class="OWAAutoLink" previewremoved="true">http://electronotes.netfirms.com/EN197.pdf</a></span><br>
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<p class="MsoNormal"><span style="font-size:14.0pt;line-height:107%;font-family:
"Arial",sans-serif">[See pages 27-33.]
<span style="mso-spacerun:yes"> </span>The warping is tangential, not hyperbolic tangential.<span style="mso-spacerun:yes">
</span><span style="mso-spacerun:yes"> </span>It is easy to see (absent a clear statement of the application involved), how confusion comes about.</span>
<o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:14.0pt;line-height:107%;font-family:
"Arial",sans-serif">Neil above is also likely correct that the original questioner was not thinking digital filter but some sort of analog ladder filter.
<span style="mso-spacerun:yes"> </span>(When we hear “ladder” we tend to think Moog Ladder or cascaded 4-pole, although digital ladder filters, “lattice” filters, and leap-frog-ladders are found digitally.
<span style="mso-spacerun:yes"> </span><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:14.0pt;line-height:107%;font-family:
"Arial",sans-serif">But why would anyone propose to correct a high-end tracking error of a FILTER with a method (tanh) that is not even used for a VCO?<span style="mso-spacerun:yes">
</span>I’m missing something. <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:14.0pt;line-height:107%;font-family:
"Arial",sans-serif">- Bernie<o:p></o:p></span></p>
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"Arial",sans-serif"><o:p> </o:p></span></p>
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