xcorr

Computes discrete auto or cross correlation

Calling Sequence

[c [,lagindex]] = xcorr(x [,maxlags [,scaling]])
[c [,lagindex]] = xcorr(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=xcorr(x) computes the un-normalized discrete auto correlation: and return in c the sequence of auto correlation lags with n is the length of x
• xcorr(x,y) computes the un-normalized discrete cross correlation: and return in c the sequence of auto correlation lags with n is the maximum of x and y length’s.

If the maxlags argument is given xcorr returns in c the sequence of auto correlation 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 auto correlation lags .

Method

This function computes using ifft(fft(x).*conj(fft(y))).

Examples

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

See Also

• `xcov`_
• `corr`_
• `fft`_

Authors

• Serge Steer, INRIA

Used Functions

`fft`_

History

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