MATLAB: Butterworth Notch Filters

Question

I'm designing a simple 60 Hz butterworth notch filter like this

[b a] = butter(n, [59 61]./(fs/2), 'stop');

When I use fvtool to look at the magnitude and phase response everything looks fine until I make n>=5, then both responses start to go all of the place. My magnitude response no longer looks like a notch.

My suspicion is that there is some roundoff error going on somewhere , but I'm unsure. Also, on my machine

>> eps
ans =
    2.22044604925031e-16

Thanks for any help.

Answer 1

For higher order filters (possibly starting as low as order 8), numerical problems due to roundoff errors may occur when forming the transfer function using the [b,a] syntax. You can avoid this by using the [z,p,k] syntax to design IIR filters. Here is an example:

[z p k] = butter(10, [59 61]./(fs/2), 'stop'); % 10th order filter
[sos,g]=zp2sos(z,p,k); % Convert to 2nd order sections form
h=dfilt.df2sos(sos,g); % Create filter object
fvtool(h);