xcov.m

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function [xycov,lags] = xcov(x,y,option1,option2)
%XCOV   Cross-covariance function estimates.
%   The cross-covariance is the cross-covariance function of
%   two sequences with their means removed.
%   XCOV(A,B), where A and B are length M vectors, returns the
%   length 2*M-1 cross-covariance sequence in a column vector.
%   XCOV(A), when A is a vector, is the auto-covariance sequence.
%   XCOV(A), when A is an M-by-N matrix, is a large matrix with
%   2*M-1 rows whose N^2 columns contain the cross-covariance
%   sequences for all combinations of the columns of A.
%   The zeroth lag of the output covariance is in the middle of the 
%   sequence, at element or row M.
%
%   XCOV(A,B,MAXLAG) computes the (cross) covariance over the
%   range of lags:  -MAXLAG to MAXLAG, i.e., 2*MAXLAG+1 lags.
%   If missing, default is MAXLAG = M-1.
%   [C,LAGS] = XCOV returns a vector of lag indices (LAGS).
%   
%   XCOV(A,'flag'), XCOV(A,B,'flag') or XCOV(A,B,MAXLAG,'flag') 
%   normalizes the covariance according to 'flag':
%       biased   - scales the raw cross-covariance by 1/M.
%       unbiased - scales the raw covariance by 1/(M-abs(k)), where k 
%                  is the index into the result.
%       coeff    - normalizes the sequence so that the covariances at 
%                  zero lag are identically 1.0.
%       none     - no scaling (this is the default).
%   
%   See also XCORR, CORRCOEF, CONV and XCORR2.

%   Author(s): L. Shure, 1-9-88
%   Copyright (c) 1988-98 by The MathWorks, Inc.
%   $Revision: 1.10 $  $Date: 1997/12/02 18:37:05 $

%   References:
%     [1] J.S. Bendat and A.G. Piersol, "Random Data:
%         Analysis and Measurement Procedures", John Wiley
%         and Sons, 1971, p.332.
%     [2] A.V. Oppenheim and R.W. Schafer, Digital Signal 
%         Processing, Prentice-Hall, 1975, pg 539.

[mx,nx] = size(x);
if nargin == 1
    [xycov,l] = xcorr(x-ones(mx,1)*mean(x));
elseif nargin == 2
    if isstr(y)|(~isstr(y)&length(y)==1)
        [xycov,l] = xcorr(x-ones(mx,1)*mean(x),y);
    else
        [my,ny] = size(y);
        [xycov,l] = xcorr(x-ones(mx,1)*mean(x),y-ones(my,1)*mean(y));
    end
elseif nargin == 3
    [my,ny] = size(y);
    if length(y)==1
        [xycov,l] = xcorr(x-ones(mx,1)*mean(x),y,option1);
    else
        [xycov,l] = xcorr(x-ones(mx,1)*mean(x),y-ones(my,1)*mean(y),option1);
    end
elseif nargin == 4
    [my,ny] = size(y);
    [xycov,l] = xcorr(x-ones(mx,1)*mean(x),y-ones(my,1)*mean(y),...
                         option1,option2);
end
if nargout > 1
    lags = l;
end