how to reduce the execution time of xcorr() function?

I want to find the windowed correlation values of x & y having array size of 1*20000. Xcorr function taking too much time to execute. Is there any way to reduce the execution time. The code is given below

k=1;
for i=1:stepsize:(length(x)-w+1)
    corrValue_w=xcorr(x(i:i+w-1),y(i:i+w-1));
    maxCorrValue_w(k)=max(corrValue_w);
    k=k+1;
end

[KSSV]

YOu reshape your data and use xcorr at once.

[Sangeetha R]

Thank you for your reply!

Can you please elaborate. I want to extract the maximum correlation value from each window.

[Jan]

This does not work:

C      = xcorr(reshape(x, w, :), reshape(y, w, :));
result = max(C, [], 1);

[Sangeetha R]

Is there any way to reshape the matrix with a given step size.

For example, input_mat=1:8;

w=4;stepsize=2;

output = [1 3 5

2 4 6

3 5 7

4 6 8]

[Jan]

This can be done easily with a loop, or with the buffer command: https://www.mathworks.com/help/signal/ref/buffer.html

[Sangeetha R]

Thank you very much.

I think, using loop will take more time to execute in case of large vectors. Buffer function solved my problem.

idx = buffer(x,w,stepsize,'nodelay');

I also got another solution for this problem mentioned below:

idx = bsxfun( @plus, (1:w).', 0:stepsize:(numel(x)-w));

[Jan]

@Sangeetha R: Please post this as an anser and "accept" it as solution.

Answer 1

[Sangeetha R]

@Jan, KSSV. Thank you so much for the solutions provided.

Solution for the problem asked is provided below;

Input matrix x & y reshaped using buffer function or bsxfun and perform the correlation at once.

% 1. Generate indexing matrix

idx = buffer(x,w,stepsize,'nodelay'); 

or

idx = bsxfun( @plus, (1:w).', 0:stepsize:(numel(x)-w));
% 2. Reshape the input matrix 
x1 = x(idx); 
y1 = y(idx);
% 3. Find the correlation of each column of x1 to that of y1
corrLength=2*w - 1
xcorr_value = fftshift(ifft(fft(x1,corrLength).*conj(fft(y1,corrLength))),1); 
% 4.  Find the maximum value from each column of xcorr_value
maxCorrValue_w = max(xcorr_value,[],1);