How can I compute the cross-correlation of two signals after using Inverse Fourier Transform

Dear all,

In Hankel matrix computaion, how can i compute the cross-correlation function from the inverse fourier transfrom of a cross-power spectra of two signals?

My interest is to get the cross-correlation of two signals that have equal dimension, where the cross-power spectra between the two signals is computed. I want to get the cross-correlation by using the inverse Fourier transform to transform it back to time-domain. The step I used to get the Inverse Fourier Transform is written below.

% Signals of interest with equal dimension

x=Signal1;

y=Signal2;

% Cross Power Spectral Density

[CxPSD, Cxfreq] = cpsd(x,y,[],[],[],fs);

% Inverse Fourier Transform

[inv_FFT] = ifft(CxPSD);

After computing the inverse fourier transform, I get one vector. Is that mean the inverse Fourier transform will be equivalent to cross-correlation between the two signals in time domain? or I am missing something?

Thanks in advance for your answer.

Regards,

Abdurehman