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Справка Scilab >> Signal Processing > Convolution - Correlation > xcorr

xcorr

Computes discrete auto or cross correlation

Syntax

[c, lagindex] = xcorr(x)
[c, lagindex] = xcorr(x, y)
[c, lagindex] = xcorr(.., maxlags)
[c, lagindex] = xcorr(.., 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:

    {\begin{matrix}C_k = \sum_{i=1}^{n-k}
                      {x_{i+k}*x^{*}_i}, k \geq 0 \\ C_k = C^{*}_{-k}, k \leq
                      -1\end{matrix}.$

    and return in c the sequence of auto correlation lags Ck=-n:n where n is the length of x
  • xcorr(x,y) computes the un-normalized discrete cross correlation:

    {\begin{matrix}C_k = \sum_{i=1}^{n-k}
                      {x_{i+k}*y^{*}_i}, k \geq 0 \\ C_k = C^{*}_{-k}, k \leq
                      -1\end{matrix}}.$

    and return in c the sequence of auto correlation lags Ck=-n:n where n is the maximum of x and y lengths.

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

The corr function computes the "biased" covariance of x and y and only return in c the sequence of auto correlation lags Ck≥0.

Method: This function computes C 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 — Computes discrete auto or cross covariance
  • corr — correlation, covariance
  • fft — fast Fourier transform.

History

ВерсияОписание
5.4.0 xcorr added.
Scilab Enterprises
Copyright (c) 2011-2017 (Scilab Enterprises)
Copyright (c) 1989-2012 (INRIA)
Copyright (c) 1989-2007 (ENPC)
with contributors
Last updated:
Thu Feb 14 15:04:59 CET 2019