Phase distortion near nyquist frequency

[truva]

Hello all,

I obtained transfer function of a 8th order low-pass butterworth filter by bilinear transformation with frequency prewarping. When I plot the phase response of the filter for a given interval of frequency there are spreaded points near Nyquist frequency. (I used unwrap.m before plotting). What is the reason of this?

I also followed a different path: First defined an impulse (delta) function in the time domain and filtered it. And I used fft to obtain the transfer function. (I took into consideration the time shift effect)

The two methods gave the same phase response except at near the Nyquist frequency. Both of them included some spreaded points near Nyquist frequency. Can you tell me what is this?

I should add that the situation gets worst with the increasing order of the filter. And first method has lesser distorsion.

 

[truva]

When I use high-pass filter same thing happened at near zero frequency not at Nyquist frequency. Hence in both cases distortion is in stop band where the gain is about 1e-15. Therefore I can say that it is not a problem.

But I don't know the reason. May be it is beause of bilinear approximation or fft is making all the mess. I don't know but it is not important any more as I said.