crosscorr.m

% Computes the normalized cross-correlation (formula 5.3 from Billings, SA (2013)) between the signals x and y.
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% written by: Renato Naville Watanabe 
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% [phi, lags, CB] = crosscorr(x,y, alpha)
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% Inputs:
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%   x and y: vector of floats, column-vectors with the signals to compute the cross-correlation.
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%   alpha: float, significance value of the confidence boundaries. Usually is used alpha = 0.05.
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% Outputs:
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%   phi: vector of floats, the normalized crosscorrelation.
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%   lags: vector of integers, vector with the corresponding lags of the phi vector.
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%   CB: vector of 2 float elements, confidence boundaries to consider that the cross-correlation at a given value is zero.

function [phi, lags, CB] = crosscorr(x,y, alpha)
    [c, lags] = xcorr(x - mean(x), y - mean(y), 'biased');
    phi = c/(std(x-mean(x), 1)*std(y-mean(y), 1));
    N = length(x);
    CB = [-norminv(alpha/2,0,1)/sqrt(N) norminv(alpha/2,0,1)/sqrt(N)];   
end