MATLAB: Cross correlation between complicated signals and measure the delay between them

corcoeffcorrelationcross_correlationMATLABxcor

excuse me, im very new in matlab and have just been strugling for half a year, and my problem is i cant find the delay i need from 2 different signals with correlation method from matlab. These signals are from 2 different transducers, so it would be a little bit difference in shape. so my idea is to give it a hilbert envelope then correlate them with 'corcoeff; but it still didnt give the result i hope for which in case ive been done it manually wtih osciloscope. i attached some files here (in zip) that contains with some of my impulses from signal 1 and signal 2 with .wav format, and the result it should give is about 10.19 micro second for delay between impulse1a and impulse2a and 10.19 us for delay between impulse1b and impulse2b. i really appreacite for helping me to solve this mystery that haunt me for a long time, or maybe theres another method for finding the delay between them in my only case?. Thank you in advance ..

Best Answer

You can use the following code to get the time delay between two signals:
clearvars
close all
clc
[y1,fs1] = audioread('impulse1a.wav');
[y2,fs2] = audioread('impulse1b.wav');
[y3,fs3] = audioread('impulse2a.wav');
[y4,fs4] = audioread('impulse2b.wav');
% Get delays for all combinations
delay12 = getDelay(y1,y2,fs1);
delay13 = getDelay(y1,y3,fs1);
delay14 = getDelay(y1,y4,fs1);
delay23 = getDelay(y2,y3,fs1);
delay24 = getDelay(y2,y4,fs1);
delay34 = getDelay(y3,y4,fs1);
%%% Subfunction
function [delayTime,delaySamples] = getDelay(x1,x2,fs)
% Functions must have same sampling frequency
t = (0:length(x1)-1)*fs; % time vector
% make sure they are the same length
len = min(length(x1),length(x2));
x1 = x1(1:len);
x2 = x2(1:len);
[r,lags] = xcorr(x1,x2); % get the cross-correlation and view the lags
figure
stem(lags,r)
xlabel('Lags [samples]')
ylabel('Cross-correlation')
[~,maxlags] = max(abs(r)); % position of maximum lag
delaySamples = lags(maxlags); % number of samples difference
delayTime = delaySamples/fs; % convert to time 
y3 = circshift(x2,lags(maxlags)); % shift the sample
% View the raw data and the shifted sample
% Notice how x3 lies on top of x1 nicely
figure
plot(t,x1,t,x2,t,y3)
xlabel('Time [s]')
legend('x1','x2','Shifted x2')
fprintf('\nSignal 2 lags behind Signal 1 by ~%.1f microseconds\n',1e6*abs(delayTime))
end
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