#### Topic: Application of normalized cross-spectrum on 1-D sine signals

Dear all

I am working on phase correlation to coregister signals (as well as to meassure relative shift) as suggested in IEEE paper by Leprince et al., 2007. I am trying to apply equations 19,20,21 and 22 on I-D sin functions having same frequency and amplitude but differ with relative phase of 108 degrees. My Matlab code is given in the mail below. The senario that I am trying to simulate is that i am sampling the two signals at 1000 samples/sec. And the difference in the phase is 108 degs that corresponds to a shift of 4 samples (i.e. The signal two (Y2) is 4 steps a head than signal 1 (Y1)). Now in this condition the peak correlation according to inverse of fourier transform of normalized cross-spectrum should be at index 4. But my code in matlab is not working as I understood the theory of Eq 22 in the paper.

Fs=1000; %samples per sec

N=[1:1000]; %Total number of samples

Y1=sin(2*pi*100*(1/Fs)*N); %Signal of 100 Hz starts at 0 phase

Y2=sin(((pi/180)*108)+2*pi*100*(1/Fs)*N); %Signal of 100 Hz starts at 108 phase

F1=fft(Y1,1024); % Fourier transform of Y1

C2=conj(fft(Y2,1024)); % Conjugate of Fourier transform of Y2

NU=F1.*C2;

DE=abs(NU);

R=NU./DE; %Normalized cross spectrum

RESULT=ifft(R,1024); %Inverse FFT of normalized cross spectrum dirc delta function

[V IND]=max(RESULT) % location of peak correlation

Kind regards