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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)```

• xcorr — Computes discrete auto or cross correlation
• corr — correlation, covariance
• fft — Transformée de Fourier discrète rapide.

History

 Report an issue << sincd Traitement du Signal FFTW >>

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