# Spectral analysis of a cross correlation function [duplicate]

So it's widely known that the Cross Correlation of 2 signals helps us in figuring out the time delay in those signals by analyzing the peak of the correlation coefficient in the time domain.

For something I am working on, due to a short baseline in comparison to the wavelength of the signal in between two of my receivers, the cross correlation of the signals from my two sensors give a peak at zero which makes it hard for me to analyse them.

Which is what brings me to my original question i.e What if I analyse the fft of this correlation coefficient array? Will I find anything hinting towards the time delay?

If not, is there anyway to figure out how I can find the time delay with such a short baseline (~50m) for a long wavelength (~20km) signal? Thanks for the help. Any little help would be appreciated.

## 1 Answer

cross-correlation would determine the time-delay. but the scale of signals' length and the delay value should be considered precisely. I mean if you have two long signal of, for say, 100sec and you are looking for a time delay in an order of 1msec, you don't need to do cross-correlation over the whole 100sec. Instead, choose a proper window time (in msec order) of two signal and then perform the cross-correlation.

• Well, my signal is 100 seconds long and the delay I want to measure is around 3-4 seconds. Windowing would be difficult because I wouldn't know what to ignore and what to keep. – Sanika Khadkikar Jun 14 '20 at 4:21
• Could I understand anything by looking at the spectrum of the cross correlation coefficient? – Sanika Khadkikar Jun 14 '20 at 4:22
• A time-shift (delay) in time-domain would represent as a phase rotation in freq-domain. I'm not sure about the spectrum of cross-correlation, but you can evaluate and compare the phase information of fourier-transform of individual signals. take for example the fourier-transform of a sin and cos (two similar signal with a delay difference) signals with a same frequency; the absolute value of both are the same in frequency domain while the phase of their fourier transform are different. – Hamid R. Tanhaei Jun 14 '20 at 8:51