# wsst

Wavelet synchrosqueezed transform

## Syntax

## Description

returns the
wavelet synchrosqueezed transform, `sst`

= wsst(`x`

)`sst`

, which you use to examine data
in the time-frequency plane. The synchrosqueezed transform has reduced energy smearing when
compared to the continuous wavelet transform (CWT). The input, `x`

, must
be a 1-D real-valued signal with at least four samples. `wsst`

computes
the synchrosqueezed transform using the analytic Morlet wavelet.

The `wsst`

function normalizes the analyzing wavelets to preserve the
L1 norm. For more information, see Algorithms.

`[___] = wsst(`

uses
a `x`

,`ts`

)`duration`

`ts`

with
a positive, scalar input, as the sampling interval. The duration can
be in years, days, hours, minutes, or seconds. If you specify `ts`

and
the `f`

output, `wsst`

returns
the frequencies in `f`

in cycles per unit time,
where the time unit is derived from specified duration.

`[___] = wsst(___,`

uses
the analytic wavelet specified by `wav`

)`wav`

to compute
the synchrosqueezed transform. Valid values are `'amor'`

and `'bump'`

,
which specify the analytic Morlet and bump wavelet, respectively.

`wsst(___)`

with no output arguments plots the synchrosqueezed
transform as a function of time and frequency. If you do not specify a sampling
frequency, `fs`

, or interval, `ts`

, the
synchrosqueezed transform is plotted in cycles per sample. If you specify a sampling
frequency, the synchrosqueezed transform is plotted in Hz. If you specify a sampling
interval using a duration, the plot is in cycles per unit time. The time units are
derived from the duration.

`[___] = wsst(___,`

returns
the synchrosqueezed transform with additional options specified by
one or more `Name,Value`

)`Name,Value`

pair arguments.

## Examples

## Input Arguments

## Output Arguments

## Algorithms

The `wsst`

function normalizes the analyzing wavelets to preserve the
L1 norm. An equivalent way to state this is that `wsst`

does not multiply
the Fourier transforms of the wavelet bandpass filters by the square root of the scale.
Multiplying by the square root of the scale would unequally weight different bandpass
contributions.

With L1 normalization, if you have equal amplitude oscillatory components in your data at
different scales, they will have equal magnitude in the CWT. The `cwt`

function also uses L1 normalization. For more information, see L1 Norm for CWT.

## References

[1] Daubechies, Ingrid, Jianfeng Lu, and Hau-Tieng Wu. “Synchrosqueezed Wavelet Transforms:
An Empirical Mode Decomposition-like Tool.” *Applied and Computational Harmonic
Analysis* 30, no. 2 (March 2011): 243–61.
https://doi.org/10.1016/j.acha.2010.08.002.

[2] Thakur, Gaurav, Eugene Brevdo, Neven S. Fučkar, and Hau-Tieng Wu. “The Synchrosqueezing
Algorithm for Time-Varying Spectral Analysis: Robustness Properties and New Paleoclimate
Applications.” *Signal Processing* 93, no. 5 (May 2013): 1079–94.
https://doi.org/10.1016/j.sigpro.2012.11.029.

## Version History

**Introduced in R2016a**