Comb Filters

The basic comb filter is given by

>> L = 16;
>> r = 0.995
>> [b,a] = comb(r,L);
>> [z,p,k] = tf2zp(1,b); % IIR comb
>> zplane(z,p)

IIR comb

>> [h,w] = freqz(1,b);
>> plot(w/pi,abs(h));
>> xlabel 'Normalized frequency (Nyquist==1)'
>> ylabel 'Magnitude Response'
>> wavwrite(y,'comb.wav');

FIR comb

>> [h,w] = freqz(b,1);
>> plot(w/pi,abs(h));
>> ylabel 'Magnitude Response'
>> xlabel 'Normalized frequency (Nyquist==1)'

Matlab code for comb filter

function [b,a] = COMB(r,L)
%  COMB
%
%      [b,a] = COMB(r,L)
%
%    generates L zeros equally spaced around a circle of radius r


b = [1 zeros(1,L-1) -r^L];
a = [1 zeros(1,L-1)]; 

Plucked-string filters

An IIR comb filter is the start of a simulation of plucked string, like a guitar string.

>> r =0.9995
>> L = 75
>> fs = 22050
>> [b,a] = comb(r,L)
>> y = filter(1,b,im);
>> wavwrite(y,fs,'comb2.wav');

The impulse response of a IIR comb is a periodic sequence of impulses at the fundamental frequency fs/L that decays at a rate determined by r. If you listen to the comb impulse, that's what you hear, a buzzy sound with pitch fs/L that dies away.

What we are missing is that the different frequency components produced by a vibrating string die away at different rates. The high frequencies die away much faster than the low frequencies. We can simulate this effect by inserting a lowpass filter in the feedback loop:

>> b = [1 1]/2;
>> a = [1 zeros(1,L-1) -r^L*b ];                                                                                              
>> ys = filter(b,a,im);
>> ys = ys/max(abs(ys));
>> wavwrite(ys,fs,'comb3.wav');

Maintained by John Loomis, last updated 6 Nov 1997