Filtering a frequency and its harmonics (Matlab)

Question

I want to remove all the frequency components from a .wav file except those within \$\pm 25\$ of \$523 \ Hz\$ as well as its harmonics.

Attempt:

I used a high pass filter first to suppress frequencies below 523 - 25 Hz. Then I used a low pass filter to suppress frequencies higher than 523 + 25. If my method is correct, is there a more efficient way of doing this?

Also, to take into account the harmonics, I used a 'for loop'. Is that right? But it only removes up to a certain harmonic. Is it possible to modify this code so that it repeats the procedure for all of the harmonics of 523 Hz, up to the Nyquist frequency?

Here's my Matlab code:

[s, Fs] = wavread('chord.wav');

wavplay(s, Fs);

n=input('Number of harmonics? ');

for N=2:1:n

% High-pass filter

FsNorm =  (523-25).*N / (Fs/2);
[b, a] = butter(10, FsNorm, 'high');
sHigh = filtfilt(b, a, s);

% Low pass filter
FsNorm = (523+25).*N / (Fs/2);
[b,a] = butter(10, FsNorm, 'low');
sLow = filtfilt(b, a, s);

end

wavplay(sLow,Fs);

Answer 1

1. Your approach will probably work okay, but for this narrow a pass-band you should probably use a designed band-pass filter rather than a combination of series low-pass and high-pass filters, particularly if you want to retain the features of the Butterworth design (maximally flat pass-band).

2. It appears that your intention is to apply each filter to the output of the previous filter, but it doesn't appear that your Matlab code does that. It applies one filter and throws away the result. Then applies another filter and throws that result away. Finally it returns the output of the final filter appplied to the input signal. So basically you only get the result from applying the final low-pass filter to the input signal.

3. Even if you did apply all the filters to the outputs of the previous filter, your first filter that suppresses frequencies above 548 Hz has removed all the harmonics (at 1046 Hz, 1569 Hz, ...), so there's no content there for the higher harmonic filters to pass through. Also, the 2nd-harmonic filter that supresses content below 1021 Hz will eliminate the fundamental signal that you passed through in the first filter.

   One option is, instead of applying each (band-pass) filters to the output of the previous filter, apply each filter to the original input signal, then sum all the filter outputs together to form the final output.

It only removes up to a certain harmonic. Is it possible to modify this to remove all harmonics of 523 Hz there is, up to the Nyquist frequency?

Yes, choose N large enough to include all the harmonics up to the Nyquist frequency.