Can the XCOV function return a result that is both unbiased and normalized?

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Muhammad - 2021-03-18T11:04:05+00:00
Question: Can the XCOV function return a result that is both unbiased and normalized?

The XCOV function in the Signal Processing Toolbox 6.8 (R2007b) has four distinct options: 'biased', 'unbiased', 'coeff', and 'none'. I would like to be able to create unbiased estimates of the cross-covariance function of my sequence with a normalized zero lag term.  

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    • Expert Answer

    Profile picture of John Michell John Michell answered . 2025-11-20

    The ability to create estimates of the cross-covariance function that are both unbiased and normalized is not available in the Signal Processing Toolbox.
     
    To work around this issue, create unbiased estimates and normalize by the zero lag term manually, as in the following example:
     
    ww = randn(1000,1);

N = 10;

[cov_ww,lags] = xcov(ww,N,'unbiased');

cov_ww = cov_ww / cov_ww(N+1);

stem(lags,cov_ww)


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