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. The wsst
function 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 magnitude of 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 arguments.Name=Value
)
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