[SOLVED] Band Stop Filter -- frequency transformation

Hello,
I'm working on a Python script to obtain the poles and zeros for classical analog filters and ultimately transform them to digital filters using the bilinear transform.
Everything works, except the Band Stop Filter code.

For BSF I used this frequency transformation: S -> Ω₀s/(Q(s² + Ω₀²))
I transform each normalized pole to two poles and two zeros at ±jΩ₀
This is the result: , and it's wrong because it looks like a single frequency notch.

For bandpass filter, using the transfomation: S -> (Q(s² + Ω₀²)) / (Ω₀s), the result is correct:


Both filters were Butterworth, 6th order, with Ω1 = 40, Ω2 = 50, Q=√Ω1Ω2/(Ω2 - Ω1).

Probably it would be easier to group the poles of the normalized low pass filter into 1st or 2nd order sections from the begining, and denormalize those according to the formulas, but I think in software is easier keeping the poles separate and grouping them at the end.

Do you know if a BSF needs a special procedure for frequency transformation?

Thanks for your help

Hi Eugen,

I'm not sure that the result is wrong.
(It is expectad that all the zeros are at the same frequency.)
Observe that it seems that the 3-dB points are in its correct location.
Could you plot the result in linear scale rather than in dB?
Regards

Z

Thanks for the response.

Indeed, with a linear scale it looks better -
It is correct -- I was expecting a constant attenuation in the stop band, but the zeros are all at the central frequency and the maximum attenuation should be at the central frequency.

Edit: Both characteristics on the same graph:

OK, now it looks like maximum planarity at the center of stopband.
The bandpass plotted in linear scale should look complementary of this one.
Regards
Z