I have recorded a signal, which I know is periodic (apart from noise). The period length is unknown. I want to extract the last period from the signal. Before going to a noisy signal, I first tested the method on a self-created noiseless signal. I've read that the autocorrolation is the way to do this, but it did not work for my example. Let me show you what I have done.
First I created a periodic signal of 1000 samples with the Matlab code below:
N_period = 1000; start_time = 0; end_time = 1; dt = (end_time-start_time)/N_period; fs = 1/dt; %sample frequency t = start_time:dt:end_time-dt; y_period = sin(2*pi*t);
I then extended the signal in order to be longer than one period, but smaller than 2 periods:
y = [y_period(0.7*N_period:N_period), y_period];
I know, by construction, that I need to get the last 1000 samples to extract the last period out of the signal.
I first pad the signal with zeros, and then apply the autocorrelation
y_cor = [zeros(1,N), y, zeros(1,N)]; [autocor, lags] = xcorr(y_cor); figure; plot(lags, autocor) grid
As can be seen in the figure below, the second largest peak appears at lag=946 and not at lag=1000.
If the method does not work for a noiseless signal, how can it then work on a noisy signal? Did I do something wrong? How can I improve this?