A speech recording includes an echo caused by reflection off a wall. Use autocorrelation to filter it out.
In the recording, a person says the word MATLAB®. Load the data and the sample rate, .
load mtlb % To hear, type soundsc(mtlb,Fs)
Model the echo by adding to the recording a copy of the signal delayed by samples and attenuated by a known factor : . Specify a time lag of 0.23 s and an attenuation factor of 0.5.
timelag = 0.23; delta = round(Fs*timelag); alpha = 0.5; orig = [mtlb;zeros(delta,1)]; echo = [zeros(delta,1);mtlb]*alpha; mtEcho = orig + echo;
Plot the original, the echo, and the resulting signal.
t = (0:length(mtEcho)-1)/Fs; subplot(2,1,1) plot(t,[orig echo]) legend('Original','Echo') subplot(2,1,2) plot(t,mtEcho) legend('Total') xlabel('Time (s)')
% To hear, type soundsc(mtEcho,Fs)
Compute an unbiased estimate of the signal autocorrelation. Select and plot the section that corresponds to lags greater than zero.
[Rmm,lags] = xcorr(mtEcho,'unbiased'); Rmm = Rmm(lags>0); lags = lags(lags>0); figure plot(lags/Fs,Rmm) xlabel('Lag (s)')
The autocorrelation has a sharp peak at the lag at which the echo arrives. Cancel the echo by filtering the signal through an IIR system whose output, , obeys .
[~,dl] = findpeaks(Rmm,lags,'MinPeakHeight',0.22); mtNew = filter(1,[1 zeros(1,dl-1) alpha],mtEcho);
Plot the filtered signal and compare to the original.
subplot(2,1,1) plot(t,orig) legend('Original') subplot(2,1,2) plot(t,mtNew) legend('Filtered') xlabel('Time (s)')
% To hear, type soundsc(mtNew,Fs)