Cross-correlation maximum in frequency domain

I need to compute the complex cross-correlation between two signals a and b and the take only the maximum value of the cross-correlation, regardless of the lag time where this occurs. I can do it either in time domain or in frequency domain. This needs to be later incorporated in a FPGA, so I want to be efficient.

An alternative is to go to frequency domain correlation, but I would need to do

max(IFFT(FFT(a)*conj(FFT(b))))

which is probably computationally costly. Is there a way to avoid going back and forth twice to the frequency and time domain and still compute the maximum cross-correlation?

thanks

Answer 1

[vidyesh]

Hi Albert,

I understand that you want to calculate the maximum value of the cross-correlation of two signals in an efficient manner.

To accomplish this task, you can utilize the 'xcorr' function in MATLAB. This function enables the computation of the cross-correlation between two discrete-time sequences. The following code snippet demonstrates how to obtain the desired value:

val = max(xcorr(a,b)); 

It's important to note that if you intend to calculate the value using the method mentioned in the question, which involves "max(IFFT(FFT(a)*conj(FFT(b))))", you will need to apply "zero-padding" to both signals beforehand. After padding, the length of the cross-correlation between 'a' and 'b' should be equal to the sum of the lengths of 'a' and 'b' minus one (length(a) + length(b) - 1).

aa = [a zeros(1, length(b) - 1)]; 
bb = [b zeros(1, length(a)  - 1)]; 
val = max(ifft(fft(aa).*conj(fft(bb)))); 

Refer to the following documentation for more information:

• xcorr function: https://www.mathworks.com/help/matlab/ref/xcorr.html
• fft function: https://www.mathworks.com/help/matlab/ref/fft.html
• ifft function https://www.mathworks.com/help/matlab/ref/ifft.html

Hope this answer helps.

[Albert Zurita]

excellent, thank you!

[Rochelle]

Vidyesh, Within the xcorr function both x and y are converted to fft and then back to ifft after multiplication. So, by using xcorr function, I dont think it will solve the problem. It will still be computationaly expensive.