# cpsd

Cross power spectral density

## Syntax

## Description

estimates
the cross power spectral density (CPSD) of two discrete-time signals, `pxy`

= cpsd(`x`

,`y`

)`x`

and `y`

,
using Welch’s averaged, modified periodogram method of spectral
estimation.

If

`x`

and`y`

are both vectors, they must have the same length.If one of the signals is a matrix and the other is a vector, then the length of the vector must equal the number of rows in the matrix. The function expands the vector and returns a matrix of column-by-column cross power spectral density estimates.

If

`x`

and`y`

are matrices with the same number of rows but different numbers of columns, then`cpsd`

returns a three-dimensional array,`pxy`

, containing cross power spectral density estimates for all combinations of input columns. Each column of`pxy`

corresponds to a column of`x`

, and each page corresponds to a column of`y`

:`pxy(:,m,n) = cpsd(x(:,m),y(:,n))`

.If

`x`

and`y`

are matrices of equal size, then`cpsd`

operates column-wise:`pxy(:,n) = cpsd(x(:,n),y(:,n))`

. To obtain a multi-input/multi-output array, append`'mimo'`

to the argument list.

For real `x`

and `y`

, `cpsd`

returns
a one-sided CPSD. For complex `x`

or `y`

, `cpsd`

returns
a two-sided CPSD.

`[`

returns
a vector of frequencies, `pxy`

,`f`

] = cpsd(___,`fs`

)`f`

, expressed in terms
of the sample rate, `fs`

, at which the cross power
spectral density is estimated. `fs`

must be the
sixth numeric input to `cpsd`

. To input a sample
rate and still use the default values of the preceding optional arguments,
specify these arguments as empty, `[]`

.

`cpsd(___)`

with
no output arguments plots the cross power spectral density estimate
in the current figure window.

## Examples

## Input Arguments

## Output Arguments

## More About

## Algorithms

`cpsd`

uses Welch’s averaged, modified
periodogram method of spectral estimation.

## References

[1] Oppenheim, Alan V., Ronald W. Schafer, and John R. Buck.
*Discrete-Time Signal Processing*. 2nd Ed. Upper Saddle River,
NJ: Prentice Hall, 1999.

[2] Rabiner, Lawrence R., and B. Gold. *Theory
and Application of Digital Signal Processing*. Englewood
Cliffs, NJ: Prentice-Hall, 1975, pp. 414–419.

[3] Welch, Peter D. “The Use of the
Fast Fourier Transform for the Estimation of Power Spectra: A Method
Based on Time Averaging Over Short, Modified Periodograms.” *IEEE ^{®} Transactions
on Audio and Electroacoustics,* Vol. AU-15, June 1967,
pp. 70–73.

## Extended Capabilities

## Version History

**Introduced before R2006a**