System Identification Toolbox

covf

Estimate time-series covariance functions.

Syntax

• R = covf(data,M)
  R = covf(data,M,maxsize)
  

Description

data is an iddata object and M is the maximum delay -1 for which the covariance function is estimated.

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.

R is returned as an nz² -by- M matrix with entries

where is the j-th row of z and missing values in the sum are replaced by zero.

The optional argument maxsize controls the memory size as explained under Algorithm Properties.

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

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

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

Algorithm

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

spa

compare

cra