[Scilab-users] Unexpected result using horner

[Federico Miyara]

Samuel,

> Sorry, but nothing is clear to me about your statements:
>
> 1) what shows you that iir() is correct while the analpf + horner way 
> is not?

There are several reasons:

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.

b) The degree of the denominator should be 6 but when using horner it 
reduces to 3.

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.

> 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?

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.

> 3) do you have a reference about the equivalence?

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 https://en.wikipedia.org/wiki/Bilinear_transform

> 4) have you tried after simp_mode(%f)?

No, but this might be the answer considering my reply to 2). I'll try it 
later.

Thanks.

Regerds,

Federico Miyara

> Samuel
>
>
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