What should the order of my FIR filter be?

Dear all,

I'm having difficulty deciidng on the order (labelled as x) of an FIR filter. I am creating speech-shaped noise using audio files with an Nfft = 4096 & a sampling rate = 22050. When doing the following:

FIR = fir2(x,NormFrqs,MagSpect);

If the order is < Nfft (as is suggested), then when subsequently trying to use pwelch:

[spect,frqs]=pwelch(SSN, win_, overlap*Nfft, Nfft, Fs,'power');

Pwelch does not run as the window (ie. hann(Nfft) or rectwin(Nfft)) is greater than the the input sample (noise filtered through the FIR filter). Does anyone know what the solution to this is? I have tried making the order of the filter > Nfft, however, the resulting speech file is has an entirely different duration to the original audio files.

Thank you!

Answer 1

[Star Strider]

The fir2 function documentation appears to favour even-numbered filter orders. (The only MATLAB functions that I know of that calculate the order for FIR filters are kaiserord and firpmord.) It’s likely best to experiment to determine the lowest filter order that successfully matches the design requirements.

[Emilia Butters]

Thank you for your help! I've made it equal to Nfft which seems to work perfectly & aligns with the stimuli. The SSN noise seems to output many dB lower than the inputs and I've been simply increasing the dB (code below & picture attatched, shown in black) of the SSN to equal that of the inputs, which then data clips using audiowrite.

dbs = x;
sound_db = norm(SSN)/sqrt(length(SSN));
ratio = (10^(dbs/20))/sound_db;
SSNn = ratio*SSN;
[spect_signal,frqs_signal]=pwelch(SSNn, win_, overlap*Nfft, Nfft, Fs,'power');
magspect_signal = sqrt(spect_signal);

I've thus normalised the data using the following code which then decreases the dB once again (picture attatched, shown in red).

SSN_n = SSNn/max(abs(SSNn(:)));

Any idea how to remedy this?

[Star Strider]

My pleasure!

A 4096-order filter (of any sort) seems to me to be excessively inefficient. It’s likely possible to get equivalent performance with a much shorter filter.

I’d use the freqz function to determine if the filter matches the desired response, and use the filtfilt function to do the actual filtering (even with FIR filters). Use the shortest filter that creates the result you want.

I have no idea what your filter is actually doing, since that information is not presented. The ‘sampling rate’ of 22050 seems like the Nyquist frequency of a maximally-sampled audio file (default sampling rate 44100 Hz).

I also don’t know the operation you’re doing. It appears to simply attenuate the signal across the spectrum, rather than doing any actual filtering, although the unfiltered spectrum is also not presented in the context of the filtered spectrum.

[Emilia Butters]

Thanks for your response! I am trying to filter white gaussian noise so that it has the same spectrum as that of the average of multiple audio files. I have used the following code to do so using an LTASS function which in turn uses pwelch. Would you suggest resampling the audio files initially?

speechfolder = '/Users/Emilia/Desktop/sounds/';
Fs = 22050;
Nfft = 4096;
[spect,frqs] = LTASS(speechfolder, Nfft, Fs);
MagSpect = sqrt(spect);
Mx = max(MagSpect);
MagSpect = MagSpect./Mx;
Nyq = Fs/2;
NormFrqs = frqs./Nyq;
FIR = fir2(Fs,NormFrqs,MagSpect);
npts = length(Nfft);
noise = wgn(npts,1,0);
SSN = conv(noise,FIR_LTASS);
win_ = hann(Nfft);
overlap = 0;
[spect_SSN,frqs_SSN]=pwelch(SSN, win_, overlap*Nfft, Nfft, Fs,'power');
magspect_SSN = sqrt(spect_SSN);

[Star Strider]

My pleasure.

I wouldn’t resample them unless they’re digitised with an inconstant sampling interval. If the sampling intervals are all very close to being the same, there is no benefit to resampling, expecially since they appear to be audio files.

I’m not certain what to suggest at this point.

[Emilia Butters]

Thank you for your help! I have in fact found the problem which was with the inputs to be pwelch function:

pwelch(x, window, noverlap, Nfft, Fs, 'power')

For the window, I was using hanning(Nfft) instead of hanning(length(data)) so that hanning(Nfft) was virtually always greater than x & prevented pwelch from functioning.

[Star Strider]

I appreciate the update.

I will delete my Answer in a few minutes.