Echo Cancellation

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, $$F_s=7418Hz$$.

load mtlb

% To hear, type soundsc(mtlb,Fs)

Model the echo by adding to the recording a copy of the signal delayed by $$\Delta$$ samples and attenuated by a known factor $$\alpha$$: $$y(n)=x(n)+\alpha x(n-\Delta )$$. 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;

% To hear, type soundsc(mtEcho,Fs)

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)")

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 $$w$$ obeys $$w(n)+\alpha w(n-\Delta )=y(n)$$.

[~,dl] = findpeaks(Rmm,lags,MinPeakHeight=0.22);

mtNew = filter(1,[1 zeros(1,dl-1) alpha],mtEcho);

% To hear, type soundsc(mtNew,Fs)

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)")