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2023.0.0 - Português

# xcov

Computes discrete auto or cross covariance

### Syntax

[c, lagindex] = xcov(x)
[c, lagindex] = xcov(x, y)
[c, lagindex] = xcov(.., maxlags)
[c, lagindex] = xcov(.., 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 Ck=-n:n where 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 Ck=-n:n where 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 Ck=-maxlags:maxlags. If maxlags is greater than length(x), the first and last values of c are zero.

The scaling argument describes how C(k) is normalized before being returned in c:

• "biased": c=C/n.
• "unbiased": c=C./(n-(-maxlags:maxlags)).
• "coeff": c=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 Ck≥0 .

### Method

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

### Examples

t = linspace(0, 100, 2000);
y = 0.8 * sin(t) + 0.8 * sin(2 * t);
[c, ind] = xcov(y, "biased");
plot(ind, c)