Zeros on [b,a] output of butter filter

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.

Answer 1

[Star Strider]

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

Then use:

signal_filtered = filtfilt(sos,g,signal);

to do the actual filtering.

[Shaula Garibbo]

Thanks very much! I didn't know about those functions, but having read the documentation I have a better understanding of your approach now.

[Star Strider]

As always, my pleasure!

[Shaula Garibbo]

Out of curiosity, if I had to attempt to achieve a similar outcome using a windowing method for the sake of computation time, how feasible would that be? Just curious to consider if it may be worth spending time on.

[Star Strider]

Use windowing with FIR filters, not IIR filters. The fir1 function does this, my favourite approach being the kaiserord function.

Getting acceptable results from FIR filters requires long filters, and those are by definition less efficient. The most efficient filter with respect to computation time is the elliptical design. (Like the Butterworth design, it is an IIR filter.) See the documentation on ellipord and ellip for those, since the syntax differs slightly from the Butterworth filter functions.

[Shaula Garibbo]

Thank you! Being pointed in the right direction is incredibly useful.

[Star Strider]

As always, my pleasure!