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Magnitude-squared coherence

finds
the magnitude-squared coherence estimate, `cxy`

= mscohere(`x`

,`y`

)`cxy`

,
of the input signals, `x`

and `y`

.

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 magnitude-squared coherence estimates.

If

`x`

and`y`

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

returns a multiple coherence matrix. The*m*th column of`cxy`

contains an estimate of the degree of correlation between all the input signals and the*m*th output signal. See Magnitude-Squared Coherence for more information.If

`x`

and`y`

are matrices of equal size, then`mscohere`

operates column-wise:`cxy(:,n) = mscohere(x(:,n),y(:,n))`

. To obtain a multiple coherence matrix, append`'mimo'`

to the argument list.

`[`

returns
a vector of frequencies, `cxy`

,`f`

] = mscohere(___,`fs`

)`f`

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

, at which the magnitude-squared
coherence is estimated. `fs`

must be the sixth
numeric input to `mscohere`

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

.

`mscohere(___)`

with
no output arguments plots the magnitude-squared coherence estimate
in the current figure window.

`mscohere`

estimates the magnitude-squared
coherence function [2] using Welch’s
overlapped averaged periodogram method [3], [5].

[1] Gómez González, A., J. Rodríguez, X. Sagartzazu,
A. Schumacher, and I. Isasa. “Multiple Coherence Method in
Time Domain for the Analysis of the Transmission Paths of Noise and
Vibrations with Non-Stationary Signals.” *Proceedings
of the 2010 International Conference of Noise and Vibration Engineering,
ISMA2010-USD2010*. pp. 3927–3941.

[2] Kay, Steven M. *Modern Spectral
Estimation.* Englewood Cliffs, NJ: Prentice-Hall, 1988.

[3] Rabiner, Lawrence R., and Bernard Gold. *Theory
and Application of Digital Signal Processing.* Englewood
Cliffs, NJ: Prentice-Hall, 1975.

[4] Stoica, Petre, and Randolph Moses. *Spectral
Analysis of Signals.* Upper Saddle River, NJ: Prentice
Hall, 2005.

[5] Welch, Peter D. “The Use of 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, 1967, pp. 70–73.

`cpsd`

| `periodogram`

| `pwelch`

| `tfestimate`