Hello,
Been trying for hours to calculate the auto-correlation of a noise signal without using the xcorr operator and not sure if my results are right. My tutor wants us to find the auto-correlation by calculating the auto-spectra, the auto-covariance from the spectra and finaly the auto-correlation from the auto-covariance without using matlab operators. My plots show a peak at zero, which I think is positive, with the auto-correlation having a peak at zero with the max value of 1 in the vertical axis, which seems correct. Although my x-axis show the 0:N points and I don't know how to display the x-axis correct. From what I understand should be a time-axis. I'm also not sure my results are correct or it was just a coincidence. Would be good to have some feedback and tips. The code is underneath a bit long but I hope it's clear. thanks you so much. Code:
fs=11025; %sampling frequency
N=1024; %number of points
T=N/fs; %time
x=2*rand(N,1)-1; %generate noise signal
%creating a delay of signal x
d=zeros(64,1);
x_delay=cat(1,d,x);
%fft of signal x and delay
X=fft(x);
X_delay=fft(x_delay);
%windowing signal x
h=hanning(2*N);
hX=X.*h(1:N);
HX=fft(hX);
%windowing signal x_delay
H=hanning(2*length(X_delay));
hX_delay=X_delay.*H(1:length(X_delay));
HX_delay=fft(hX_delay);
%finding the auto-spectra
for i=1:N
Sxx(i)= (HX(i).*conj(HX_delay(i))/T);
end
%finding auto-covariance
Sxxt=ifft(Sxx);
%plotting the auto-covariance
subplot(4,1,2)
plot(abs(Sxxt));
title('auto-covariance')
%finding the boundary of the auto-covariance Sxx(0)
Sxx0=mean(Sxx);
%finding the auto-correlation
Rxx=Sxxt/Sxx0;
%plotting the auto-correlation
subplot(4,1,3);
plot(d,abs(Rxx));
title('auto-correlation')
