%  This script generates colored noise by filtering white noise with a
%  Butterworth bandpass filter. Figures are then generated to compare the
%  PSD of the colored noise to the filter transfer function magnitude.  In
%  addition, the autocorrelation is taken of the input white noise sequence
%  and the output colored noise sequence for comparisons.
%
%  Written by Kevin D. Donohue (donohue@engr.uky.edu) March 2004

fs = 8000;  %  Sampling Frequency
dur = 20;     %  Sound duration in seconds
ord = 6;
plen = 32;  % PSD segment length
%  Bandlimit on the filter
f1 = [500];  % lower bandlimit
f2 = [1500]; % corresponding upper bandlimit
% colors for the plots
col = ['g', 'r', 'b', 'k', 'c', 'b'];
no = randn(1,round(fs*dur));  %  Generate noise signal
[b,a] = butter(ord,2*[f1 f2]/fs);  % Generate filter
% perform filter operation to get colored noise
cno = filter(b,a,no);
% Compute the PSD
[p, fax] = pwelch(cno,hamming(plen),fix(plen/2),2*plen, fs); % Compute PSD of noise 
figure(1); lh = plot(fax,abs(fs*p/2),col(1)) % Plot PSD
set(lh,'LineWidth',2)  %  Make line thicker
hold on
%  Find filter transfer function
[h,fq] = freqz(b,a,2*plen,fs);
plot(fq,abs(h).^2,col(2)) 
hold off
% Label figure
xlabel('Hertz', 'Fontsize', 14)
ylabel('PSD', 'Fontsize', 14)

%  Compute autocorrelation of input sequence
mxlag = fs*.02;  %  Only compute lags up to 20 milliseconds
[acwno, lagwno] = xcorr(no, mxlag, 'coef');
%  Plot lags 
figure(2); plot(1000*lagwno/(fs),acwno)
xlabel('milliseconds','Fontsize', 14);  ylabel('Correlation coefficient','Fontsize', 14)

%  Compute autocorrelation of output sequence
mxlag = fs*.02;  %  Only compute lags up to 20 milliseconds
[accno, lagcno] = xcorr(cno, mxlag, 'coef');
%  Plot lags 
figure(3); plot(1000*lagcno/(fs),accno)
xlabel('milliseconds','Fontsize', 14);  ylabel('Correlation coefficient','Fontsize', 14)