xcov

Computes discrete auto or cross covariance

Calling Sequence

[c [,lagindex]] = xcov(x [,maxlags [,scaling]])
[c [,lagindex]] = xcov(x,y [,maxlags [,scaling]])

Parameters

:x a vector of real or complex floating point numbers. : :y a vector of real or complex floating point numbers. The default

value is x.

: :maxlags a scalar with integer value greater than 1. The default

value is n. Where n is the maximum of the x and y vector length.

: :scaling a character string with possible value: “biased”,

“unbiased”, “coeff”, “none”. The default value is “none”.

: :c a vector of real or complex floating point numbers with same

orientation as x.

: :lagindex a row vector, containing the lags index corresponding to

the c values.

:

Description

• c=xcov(x) computes the un-normalized discrete covariance: and return in c the sequence of covariance lags with n is the length of x
• xcov(x,y) computes the un-normalized discrete cross covariance: and return in c the sequence of cross covariance lags with n is the maximum of x and y length’s.

If the maxlags argument is given xcov returns in c the sequence of covariance lags . If maxlags is greater than length(x), the first and last values of c are zero.

The scaling argument decribes how is normalized before being returned in c:

• “biased”: c= /n.
• “unbiased”: c= ./(n-(-maxlags:maxlags)).
• “coeff”: c= /(norm(x)*norm(y)).

Remark

The `corr`_ function computes the “biased” covariance of x and y and only return in c the sequence of covariance lags .

Method

This function computes using xcorr(x-mean(x),y-mean(y),...).

Examples

t = `linspace`_(0, 100,2 000);
        y = 0.8 * `sin`_(t) + 0.8 * `sin`_(2 * t);
        [c, ind] = xcov(y, "biased");
        `plot`_(ind, c)

See Also

• `xcorr`_
• `corr`_
• `fft`_

Authors

• Serge Steer, INRIA

Used Functions

`xcorr`_

History

Version Description 5.4.0 xcov added. .. _xcorr: xcorr.html .. _corr: corr.html .. _fft: fft.html