covf - Estimate covariance functions for time-domain iddata object

Syntax

Description

cov = covf(data,max_delay) estimates the covariance for the input-output data, data, with the maximum delay - 1, max_delay.

cov = covf(data,max_delay,MaxSize) specifies the maximum size of the arrays, MaxSize, formed by the algorithm.

Let z contain the output and input channels

where y and u are the rows of data.OutputData and data.InputData, respectively, with a total of nz channels.

cov is returned as an nz² -by- max_delay matrix with entries

where z_j is the jth row of z, and missing values in the sum are replaced by zero.

The easiest way to describe and unpack the result is to use

reshape(cov(:,k+1),nz,nz) = E z(t)*z'(t+k)

Here ' is complex conjugate transpose, which also explains how complex data is handled. The expectation symbol E corresponds to the sample means.

Input Arguments

Output Arguments

Algorithms

When nz is at most two, and when permitted by maxsize, a fast Fourier transform technique is applied. Otherwise, straightforward summing is used.

See Also

cra | iddata | impulseest | spa | spafdr

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