function fcoefs=MakeERBFilters(fs,numChannels,lowFreq,width) % function [fcoefs]=MakeERBFilters(fs,numChannels,lowFreq) % This function computes the filter coefficients for a bank of % Gammatone filters. These filters were defined by Patterson and % Holdworth for simulating the cochlea. % % The result is returned as an array of filter coefficients. Each row % of the filter arrays contains the coefficients for four second order % filters. The transfer function for these four filters share the same % denominator (poles) but have different numerators (zeros). All of these % coefficients are assembled into one vector that the ERBFilterBank % can take apart to implement the filter. % % The filter bank contains "numChannels" channels that extend from % half the sampling rate (fs) to "lowFreq". Alternatively, if the numChannels % input argument is a vector, then the values of this vector are taken to % be the center frequency of each desired filter. (The lowFreq argument is % ignored in this case.) % Note this implementation fixes a problem in the original code by % computing four separate second order filters. This avoids a big % problem with round off errors in cases of very small cfs (100Hz) and % large sample rates (44kHz). The problem is caused by roundoff error % when a number of poles are combined, all very close to the unit % circle. Small errors in the eigth order coefficient, are multiplied % when the eigth root is taken to give the pole location. These small % errors lead to poles outside the unit circle and instability. Thanks % to Julius Smith for leading me to the proper explanation. % Execute the following code to evaluate the frequency % response of a 10 channel filterbank. % fcoefs = MakeERBFilters(16000,10,100); % y = ERBFilterBank([1 zeros(1,511)], fcoefs); % resp = 20*log10(abs(fft(y'))); % freqScale = (0:511)/512*16000; % semilogx(freqScale(1:255),resp(1:255,:)); % axis([100 16000 -60 0]) % xlabel('Frequency (Hz)'); ylabel('Filter Response (dB)'); % Rewritten by Malcolm Slaney@Interval. June 11, 1998. % (c) 1998 Interval Research Corporation if nargin < 4; width = 1.0; end % Scaling of bandwidths by dpwe T = 1/fs; if length(numChannels) == 1 cf = ERBSpace(lowFreq, fs/2, numChannels); else cf = numChannels(1:end); if size(cf,2) > size(cf,1) cf = cf'; end end % Change the followFreqing three parameters if you wish to use a different % ERB scale. Must change in ERBSpace too. EarQ = 9.26449; % Glasberg and Moore Parameters minBW = 24.7; order = 1; ERB = ((cf/EarQ).^order + minBW^order).^(1/order); B=1.019*2*pi*ERB*width; A0 = T; A2 = 0; B0 = 1; B1 = -2*cos(2*cf*pi*T)./exp(B*T); B2 = exp(-2*B*T); A11 = -(2*T*cos(2*cf*pi*T)./exp(B*T) + 2*sqrt(3+2^1.5)*T*sin(2*cf*pi*T)./ ... exp(B*T))/2; A12 = -(2*T*cos(2*cf*pi*T)./exp(B*T) - 2*sqrt(3+2^1.5)*T*sin(2*cf*pi*T)./ ... exp(B*T))/2; A13 = -(2*T*cos(2*cf*pi*T)./exp(B*T) + 2*sqrt(3-2^1.5)*T*sin(2*cf*pi*T)./ ... exp(B*T))/2; A14 = -(2*T*cos(2*cf*pi*T)./exp(B*T) - 2*sqrt(3-2^1.5)*T*sin(2*cf*pi*T)./ ... exp(B*T))/2; gain = abs((-2*exp(4*i*cf*pi*T)*T + ... 2*exp(-(B*T) + 2*i*cf*pi*T).*T.* ... (cos(2*cf*pi*T) - sqrt(3 - 2^(3/2))* ... sin(2*cf*pi*T))) .* ... (-2*exp(4*i*cf*pi*T)*T + ... 2*exp(-(B*T) + 2*i*cf*pi*T).*T.* ... (cos(2*cf*pi*T) + sqrt(3 - 2^(3/2)) * ... sin(2*cf*pi*T))).* ... (-2*exp(4*i*cf*pi*T)*T + ... 2*exp(-(B*T) + 2*i*cf*pi*T).*T.* ... (cos(2*cf*pi*T) - ... sqrt(3 + 2^(3/2))*sin(2*cf*pi*T))) .* ... (-2*exp(4*i*cf*pi*T)*T + 2*exp(-(B*T) + 2*i*cf*pi*T).*T.* ... (cos(2*cf*pi*T) + sqrt(3 + 2^(3/2))*sin(2*cf*pi*T))) ./ ... (-2 ./ exp(2*B*T) - 2*exp(4*i*cf*pi*T) + ... 2*(1 + exp(4*i*cf*pi*T))./exp(B*T)).^4); allfilts = ones(length(cf),1); fcoefs = [A0*allfilts A11 A12 A13 A14 A2*allfilts B0*allfilts B1 B2 gain]; if (0) % Test Code A0 = fcoefs(:,1); A11 = fcoefs(:,2); A12 = fcoefs(:,3); A13 = fcoefs(:,4); A14 = fcoefs(:,5); A2 = fcoefs(:,6); B0 = fcoefs(:,7); B1 = fcoefs(:,8); B2 = fcoefs(:,9); gain= fcoefs(:,10); chan=1; x = [1 zeros(1, 511)]; y1=filter([A0(chan)/gain(chan) A11(chan)/gain(chan) ... A2(chan)/gain(chan)],[B0(chan) B1(chan) B2(chan)], x); y2=filter([A0(chan) A12(chan) A2(chan)], ... [B0(chan) B1(chan) B2(chan)], y1); y3=filter([A0(chan) A13(chan) A2(chan)], ... [B0(chan) B1(chan) B2(chan)], y2); y4=filter([A0(chan) A14(chan) A2(chan)], ... [B0(chan) B1(chan) B2(chan)], y3); semilogx((0:(length(x)-1))*(fs/length(x)),20*log10(abs(fft(y4)))); end