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wsst

Wavelet synchrosqueezed transform

Syntax

sst = wsst(x)
[sst,f] = wsst(x)
[___] = wsst(x,fs)
[___] = wsst(x,ts)
[___] = wsst(___,wav)
wsst(___)
[___] = wsst(___,Name,Value)

Description

example

sst = wsst(x) returns the wavelet synchrosqueezed transform, 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. 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.

example

[sst,f] = wsst(x) returns a vector of frequencies, f, in cycles per sample. The frequencies correspond to the rows of sst.

example

[___] = wsst(x,fs) computes the sychrosqueezed transform using the specified sampling frequency, fs, in Hz, to compute the synchrosqueezed transform. If you specify an f output, wsst returns the frequencies in Hz. You can use any previous combination of output values.

example

[___] = wsst(x,ts) uses a 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.

example

[___] = wsst(___,wav) uses the analytic wavelet specified by 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(___,Name,Value) returns the synchrosqueezed transform with additional options specified by one or more Name,Value pair arguments.

Examples

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Obtain the wavelet synchrosqueezed transform of a speech sample using default values.

load mtlb;
sst = wsst(mtlb);

Obtain the wavelet synchrosqueezed transform of a speech signal and compare the original and reconstructed signals.

Load the speech signal and obtain its synchrosqueezed transform.

load mtlb;
soundsc(mtlb);
dt = 1/Fs;
t = 0:dt:numel(mtlb)*dt-dt;
[sst,f] = wsst(mtlb);

Plot the synchroqueezed transform.

pcolor(t,f,abs(sst));
shading interp
xlabel('Seconds'); ylabel('Amplitude');
title('Synchrosqueezed Transform');

Obtain the inverse synchroqueezed transform and play the reconstructed speech signal.

xrec = iwsst(sst);
soundsc(xrec);

Obtain and plot the wavelet synchrosqueezed transform of a quadratic chirp. The chirp is sampled at 1000 Hz.

load quadchirp;
[sst,f] = wsst(quadchirp,1000);
hp = pcolor(tquad,f,abs(sst));
hp.EdgeColor = 'none';
title('Wavelet Synchrosqueezed Transform');
xlabel('Time'); ylabel('Hz');

Obtain the wavelet synchrosqueezed transform of sunspot data using the default Morlet wavelet. Specify the sampling interval to be one year.

load sunspot.dat;
wsst(sunspot(:,2),years(1))

Obtain and plot the wavelet synchrosqueezed transform of sunspot data using the bump wavelet. Specify the sampling interval to be 1 for one sample per year.

load sunspot.dat;
wsst(sunspot(:,2),years(1),'bump')

Input Arguments

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Input signal, specified as a row or column vector. x must be a 1-D, real-valued signal with at least four samples.

Sampling frequency, specified as a positive scalar.

Sampling interval, also known as the sampling period, specified as a duration with positive scalar input. Valid durations are years, days, hours, seconds, and minutes. You cannot use calendar durations (caldays, calweeks, calmonths, calquarters, or calyears). You cannot specify both ts and fs.

Example: sst = wsst(x,hours(12))

Analytic wavelet used to compute the synchrosqueezed transform, specified as 'amor' or 'bump'. These character vectors specify the analytic Morlet wavelet and bump wavelet, respectively.

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: 'VoicesPerOctave',26

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Number of voices per octave to use in the synchrosqueezed transform, specified as the comma-separated pair consisting of 'VoicesPerOctave' and an integer from 10 to 48. The product of the number of voices per octave and the number of octaves is the number of scales. The number of octaves depends on the size of the input x and is floor(log2(numel(x)))-1.

Option to extend the input signal symmetrically, specified as the comma-separated pair consisting of 'ExtendSignal' and either false or true. Extending the signal symmetrically can mitigate boundary effects. If you specify false, then the signal is not extended. If you specify true, then the signal is extended.

Output Arguments

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Synchrosqueezed transform, returned as a matrix. By default, the synchrosqueezed transform uses floor(log2(numel(x)))-1 octaves, 32 voices per octave, and the analytic Morlet wavelet. sst is an Na-by-N matrix where Na is the number of scales, and N is the number of samples in x. The default number of scales is 32*(floor(log2(numel(x)))-1).

Frequencies of the synchrosqueezed transform, returned as a vector. The frequencies correspond to the rows of the sst. If you do not specify fs or ts, the frequencies are in cycles per sample. If you specify fs, the frequencies are in Hz. If you specify ts, the frequencies are in cycles per unit time. The length of the frequency vector is the same as the number of sst rows. If you specify ts as the sampling interval, ts is used to compute the scale-to-frequency conversion for f.

References

[1] I. Daubechies, I., J. Lu, and H. T. Wu. "Synchrosqueezed Wavelet Transforms: an Empricial Mode Decomposition-like Tool", Applied and Computational Harmonic Analysis. Vol. 30(2), pp. 243–261.

[2] Thakur, G., E. Brevdo, N. S. Fučkar, and H. T. Wu. "The Synchrosqueezing algorithm for time-varying spectral analysis: robustness properties and new paleoclimate applications." Signal Processing. Vol. 93, pp. 1079–1094.

Introduced in R2016a

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