Differences between cpsd and xcorr

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Hello, i'm having trouble with a basic signal processing problem : Correct me if i'm wrong, but theorically, calculating the inverse Fourrier transformationof a crosspower spectral density should give me teh intercorrelation, right ?
If so, i do not understand why i get diferrents results when i use :
if true
Sxy=cpsd(sigM(1,:),sigM(2,:),[],[],Nfft,24000);
A=sigM(1,:);
B=sigM(2,:);
[C,~]=xcorr(A,B,'coeff');
Rxy=real(ifftshift(Sxy));
end
Shouldn't be Rxy and C strictly the same, if i use the same fft length and sample rate ?

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