Zeros on [b,a] output of butter filter

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Shaula Garibbo 2020-1-20

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https://ww2.mathworks.cn/matlabcentral/answers/501132-zeros-on-b-a-output-of-butter-filter

评论： Star Strider 2020-1-21

Hi. I'm trying to create a low-pass filter for a large collection of audio files to make some room on my hard drives. I'm using the butter filter as follows:

          fn = fs/2;                                %(fs = 32000)
          fc = 125/fn;                              %normalised passband frequency = 0.0078
          fz = 135/fn;                              %normalised stopband frequency = 0.0084
          [n, wn] = buttord(fc,fz,3,60);            %(n = 60, wn = 0.0078)
          [b,a] = butter(n, wn, ftype);        

But the 'b' output component is always made up of zeros (I just get blank graphs on the freqz plots).

I suspect I have misunderstood something along the line, but I am overall aiming for a filter that reads in the 32kHz audio file, and removes all frequencies over 125Hz, as I do not need them for my analysis. Any advice would be greatly appreciated.

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Answer 1

Star Strider 2020-1-20

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The filter is unstable. This can easily be remedied by converting to zero-pole-gain realization, and then second-order section implementation:

ftype = 'low';
fs = 32000
fn = fs/2;                                %(fs = 32000)
fc = 125/fn;                              %normalised passband frequency = 0.0078
fz = 135/fn;                              %normalised stopband frequency = 0.0084
[n, wn] = buttord(fc,fz,3,60);            %(n = 60, wn = 0.0078)
[z,p,k] = butter(n, wn, ftype);         % Use Zero-Pole-Gain Representation
[sos,g] = zp2sos(z,p,k);                % Second-Order Section For Stability
figure
freqz(sos, 2^14, fs)                        % Filter Bode Plot