Hello,
I understand that you are trying to modify the given implementation of "xcorrFD" function to include the normalization option in the frequency domain, and expecting the result obtained from MATLAB's built-in "xcorr" function.
The following example demonstrates how you can include the normalization (where the cross-correlations at zero lag are identically 1.0):
% Generate input signals
x = [1, 1, 1, 1];
y = [1, 1, 1, 1];
% Calculate the cross-correlation with normalization
[lags, ck_custom, td_custom] = xcorrFD(x, y, true); % see the function definition at the bottom of the script
% Calculate the cross-correlation using MATLAB's "xcorr" function with normalization
[ck_matlab, lags_matlab] = xcorr(x, y, 'normalized');
disp('Cross-correlation result:');
disp(ck_custom);
disp('Lags:');
disp(lags);
% Plot the input signals and the cross-correlation result
figure
subplot(3,1,1);
stem(x);
xlabel('Sample index');
ylabel('Amplitude');
title('Signal x');
subplot(3,1,2);
stem(y);
xlabel('Sample index');
ylabel('Amplitude');
title('Signal y');
subplot(3,1,3);
stem(lags_matlab, ck_matlab, 'bo');
hold on
stem(lags, ck_custom, 'r*');
hold off
legend("xcorr - MATLAB built-in function", "xcorrFD - Custom function")
xlabel('Lag');
ylabel('Cross-correlation');
title('Cross-correlation of x and y');
%% xcorrFD function definition
function [lags, ck, td] = xcorrFD(x, y, normalize)
a = y(:); % Ensure y is a column vector
b = x(:); % Ensure x is a column vector
len = length(a);
c = [a; zeros(len-1, 1)]; % Zero-padding and flipping a
d = [b; zeros(len-1, 1)]; % Zero-padding b
% Compute FFTs
X1 = fft(c);
X2 = fft(d);
% Compute cross correlation
X = X1.*conj(X2);
ck = fftshift(ifft((X)));
if normalize
ck = ck / abs(ck(len)); % Normalize to ensure magnitude at zero lag is 1
end
[~, i] = max(ck);
td = i - len;
lags = -(len-1):len-1;
end
To know more about different scaling options in "xcorr" function, you can refer to the following MathWorks documentation:
I hope this helps you to achieve the normalization in the cross-correlation performed in the frequency domain.
