% CXCORR Circular Cross Correlation function estimates. 
% CXCORR(a,b), where a and b represent samples taken over time interval T
% which is assumed to be a common period of two corresponded periodic signals. 
% a and b are supposed to be length M row vectors, either real or complex.
% 
% [x,c]=CXCORR(a,b) returns the length M-1 circular cross correlation sequence c
% with corresponded lags x.
%   
% The circular cross correlation is:
%         c(k) = sum[a(n)*conj(b(n+k))]/[norm(a)*norm(b)]; 
% where vector b is shifted CIRCULARLY by k samples.
%
% The function doesn't check the format of input vectors a and b!
function [x,c]=CXCORR(a,b)
na=norm(a);
nb=norm(b);
a=a/na; %normalization
b=b/nb;

% Normal cross correlation.
c = real(abs((ifft(((fft(a) .* fft(fliplr(b))))))));
x=[0:length(b)-1]; %lags

% Exponential Decay
%for k=1:length(b)
%    c(k)=exp(1-sum(abs(a-b)));
%    b=[b(end),b(1:end-1)]; %circular shift
%end
x=[0:length(b)-1]; %lags
