# wcoherence

Wavelet coherence and cross-spectrum

## Syntax

## Description

returns
the magnitude-squared wavelet coherence, which is a measure of the
correlation between signals `wcoh`

= wcoherence(`x`

,`y`

)`x`

and `y`

in
the time-frequency plane. Wavelet coherence is useful for analyzing
nonstationary signals. The inputs `x`

and `y`

must
be equal length, 1-D, real-valued signals. The coherence is computed
using the analytic Morlet wavelet.

`[___] = wcoherence(___,`

specifies options using one or more name-value arguments in addition to the input arguments in
previous syntaxes.`Name=Value`

)

`wcoherence(___) `

with no output
arguments plots the wavelet coherence and cone of influence in the
current figure. Due to the inverse relationship between frequency
and period, a plot that uses the sampling interval is the inverse
of a plot the uses the sampling frequency. For areas where the coherence
exceeds 0.5, plots that use the sampling frequency display arrows
to show the phase lag of `y`

with respect to `x`

.
The arrows are spaced in time and scale. The direction of the arrows
corresponds to the phase lag on the unit circle. For example, a vertical
arrow indicates a π/2 or quarter-cycle phase lag. The corresponding
lag in time depends on the duration of the cycle.

## Examples

## Input Arguments

## Output Arguments

## More About

## References

[1] Grinsted, A., J. C. Moore, and S. Jevrejeva. “Application of the Cross Wavelet
Transform and Wavelet Coherence to Geophysical Time Series.” *Nonlinear Processes in
Geophysics* 11, no. 5/6 (November 18, 2004): 561–66.
https://doi.org/10.5194/npg-11-561-2004.

[2] Maraun, D., J. Kurths, and M. Holschneider. “Nonstationary Gaussian Processes in
Wavelet Domain: Synthesis, Estimation, and Significance Testing.” *Physical Review E* 75, no. 1 (January 22, 2007): 016707.
https://doi.org/10.1103/PhysRevE.75.016707.

[3] Torrence, Christopher, and Peter J. Webster. “Interdecadal Changes in the ENSO–Monsoon
System.” *Journal of Climate* 12, no. 8 (August 1999): 2679–90.
https://doi.org/10.1175/1520-0442(1999)012<2679:ICITEM>2.0.CO;2.

## Extended Capabilities

## Version History

**Introduced in R2016a**