Cross-correlation of two complex signals using sliding dot product

Is there anyone has done cross-correlation between two complex signals (uneqal lengths) using sliding dot product without zero padding?

I am stuck on my code and I don't get correct resuts. So, if someone has done that, could you please share your code?

I don't want to use the built-in xcorr function since it does zero padding.

Answer 1

[Matt J]

If there is to be no zero-padding, what should happen when the shorter signal slides to the edge of the longer signal? Does the sliding simply stop at that point?. If so, just use convolution with the 'valid' flag,

x=rand(1,10); y=rand(1,3);

result = conv(x,flip(y),'valid')

result = 1×8

0.0594 0.7935 0.3238 0.0481 0.3591 0.7380 0.5230 0.3385

Checking the result against explicit dot products:

dot(y,x(1:3)) %the first dot product

ans = 0.0594

dot(y, x(8:10)) %the last dot product

ans = 0.3385

[Wesam AlAmiri]

I am not sure how that can be solved. We either make the length of larger signal as multiples of length of small one, but this is difficult since I am using signals generated from usrps. Or we can neglect part of the signal to make the lengths multiples.

Anyway, I tried your code with synthetic complex signal, but it does not give a single peak around the delay value (which zero) comparing to the xcorr. To simplify and make sure the code is correct, I did cross-correlation for the same signal with same length:

result=conv(x,flip(x)) 

I got the result as shown below:

Then, I did

result=xcorr(x,x)

And I got this result.

[Matt J]

For complex signals, you need to do

result=conv(x,conj(flip(x))) 

Failing that, I would need you to attach your x in a .mat file to try to reproduce what you done. Below, I get a very clear peak with my own randomly generated x. Also, you have already seen a direct quantitative comparison between conv and inner product calculations, so you know conv should correctly compute what you asked for.

x=normalize(rand(1,1000),2,'n');

plot(conv(x,flip(x)))

[Wesam AlAmiri]

Thanks, Mr. Matt!

It works now.