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<font face="Courier New">Samuel,</font><br>
<br>
<blockquote type="cite"
cite="mid:ab405210-2987-25d4-df5e-fbbd92b6d5ac@free.fr">Sorry, but
nothing is clear to me about your statements:<br>
<br>
1) what shows you that iir() is correct while the analpf + horner
way is not?<br>
</blockquote>
<br>
There are several reasons: <br>
<br>
a) The result of using iir() is consistent with the expected
frequency response, since it is equal to the analog filter response
except at high frequency, an expected artifact for IIR filters. The
other solution is completely different.<br>
<br>
b) The degree of the denominator should be 6 but when using horner
it reduces to 3.<br>
<br>
My own informal and not very deep analysis suggests that as all the
poles are very close to unity, may be horner() performs some
simplification and simplifies things incorrectly, which might
dramatically change the frequency response. <br>
<br>
<blockquote type="cite"
cite="mid:ab405210-2987-25d4-df5e-fbbd92b6d5ac@free.fr"> 2) With
the analpf + horner method, assuming that it is not correct, what
shows you that horner is not correct, while analpf is correct,
instead of the opposite or both incorrect?<br>
</blockquote>
<br>
analpf() is a very simple algorithm, at least for Butterworth, since
explicit formulas for the poles exist and in all the cases I have
tested the result is the expected one, particularly in this case. <br>
<br>
<blockquote type="cite"
cite="mid:ab405210-2987-25d4-df5e-fbbd92b6d5ac@free.fr"> 3) do you
have a reference about the equivalence?<br>
</blockquote>
<br>
The substitution of the bilinear transformation is the usual method
to get an IIR digital filter from an analog prototype. They aren't
completely equivalent, but very similar up to about half Nyquist
frequency. Any book on digital signal processing includes that
transformation. Also
<a class="moz-txt-link-freetext" href="https://en.wikipedia.org/wiki/Bilinear_transform">https://en.wikipedia.org/wiki/Bilinear_transform</a><br>
<br>
<blockquote type="cite"
cite="mid:ab405210-2987-25d4-df5e-fbbd92b6d5ac@free.fr"> 4) have
you tried after simp_mode(%f)?<br>
</blockquote>
<br>
No, but this might be the answer considering my reply to 2). I'll
try it later.<br>
<br>
Thanks.<br>
<br>
Regerds,<br>
<br>
Federico Miyara <br>
<br>
<blockquote type="cite"
cite="mid:ab405210-2987-25d4-df5e-fbbd92b6d5ac@free.fr">
<p> </p>
Samuel<br>
<br>
<br>
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