Designfilt and bandstopfir adds +320dB for some reason

Good evening!

I am trying to create a set of FIR filters (using designfilt) to apply to some audio signals, and I'm having an issue.

When I try to use a 'bandstopfir', for some reason the whole signal is amplified around +320dB (while 'bandpassfir', 'lowpassfir' and 'highpassfir' are working correctly)

Here's a quick example of the code I'm using, and I added the resulting images of each of these cases showing the issue:

clear

filterObject1 = designfilt('bandstopfir','FilterOrder',301,...
    'CutoffFrequency1',2000,'CutoffFrequency2',4000,'SampleRate',48000);


filterObject2 = designfilt('bandpassfir','FilterOrder',301,...
    'CutoffFrequency1',2000,'CutoffFrequency2',4000,'SampleRate',48000);

Here are images using fvtool to show both filter responses:

Bandstop (incorrect behaviour):

Bandpass (expected behaviour):

Is this a bug, is the installation I'm using somehow broken, or am I doing something wrong?

Answer 1

[Paul]

Hi Andres,

I don't have a complete answer, just an observation. Here's the original design with order 301

filterObject1 = designfilt('bandstopfir','FilterOrder',301,...
    'CutoffFrequency1',2000,'CutoffFrequency2',4000,'SampleRate',48000);
figure
freqz(filterObject1,0:5000,48000)
xlim([0 5])

We see the undesired result, and we see see that something peculiar is happening with the response at very low frequency.

Try again, but use an even filter order

filterObject1 = designfilt('bandstopfir','FilterOrder',300,...
    'CutoffFrequency1',2000,'CutoffFrequency2',4000,'SampleRate',48000);
figure
freqz(filterObject1,0:5000,48000)
xlim([0 5])

If you experiment, you'll see that bandstopfir doesn't like an odd filter order (in combination with the other designfilt parameters and defaults). I'm not sure why that is the case, but maybe this observation can help you move forward.

[Andres]

Thank you for the answer, this information has proven very useful to me.

Your comment made me think of trying other combinations of parameters to override the defaults, and I have noticed that both phenomenons are actually connected. The low frequency response affects the parameter "ScalePassband" which tries to bring the gain of 0Hz to 0dB.

If I set "ScalePassband" to false, the filter doesn't add any incorrect gain (although the low frequency response is still wrong), which is useful enough for my applications.

Of course there's still an issue to address, but at least this is enough for me for the moment.

Thanks!

[Paul]

I'm not sure the low frequency response is wrong.

I suspect that a bandstop, FIR filter has particular symmetry requirements on its zeros, which can be met when there's an even number of zeros. When the filter order is odd, we have an extra, lonely, real zero, and that zero ends up z = 1 (at least for this set of design parameters) which governs the low frequency response. In fact, H(j*0) = 0 in theory, so that scaling you see from the ScalePassBand parameter to 320 dB is just numerical error because H(j*0) doesn't evaluate exactly to zero.

For a bandpass filter, that extra zero for the odd order case ends up at z = -1, so only has an effect on the high frequency response, which is very small anyway. It also wouldn't matter (much) if the extra zero is at z = 1 for for the same reason.

At present, I don't know why the extra zero is at z = 1 for bandstop and z = -1 for bandpass, or if that depends on the particular design method.

[Andres]

I see.

That puts me somewhat at ease, since it would mean that it's just my lack of knowledge (which is easier to fix than an error in Matlab itself!)