waveletsupport

CWT filter bank time supports

Syntax

spsi = waveletsupport(fb)

spsi = waveletsupport(fb,thresh)

Description

spsi = waveletsupport(fb) returns the wavelet time supports, defined as the time interval in which all of the wavelet's energy occurs. The default tolerance is 99.99% of the energy. The time supports are returned in the MATLAB^® table spsi. The wavelets are normalized to have unit energy.

spsi = waveletsupport(fb,thresh) specifies the threshold for the integrated energy. The time support of the wavelet is defined as the first instant the integrated energy exceeds thresh and the last instant the integrated energy is less than 1−thresh. If unspecified, thresh defaults to 10⁻⁴.

Examples

Wavelet Filter Bank Time Supports

Create a continuous wavelet transform filter bank. Set the sampling frequency to 1000 Hz and the frequency limits to range from 100 Hz to 200 Hz. Obtain the time supports of the wavelets in the filter bank.

fb = cwtfilterbank('SamplingFrequency',1000, ...
    'FrequencyLimits',[100 200]);
spsi = waveletsupport(fb)

spsi=11×5 table
      CF      IsAnalytic    TimeSupport    Begin      End 
    ______    __________    ___________    ______    _____

       200    "Analytic"       0.032       -0.016    0.016
    186.61    "Analytic"       0.034       -0.017    0.017
    174.11    "Analytic"       0.038       -0.019    0.019
    162.45    "Analytic"        0.04        -0.02     0.02
    151.57    "Analytic"       0.042       -0.021    0.021
    141.42    "Analytic"       0.046       -0.023    0.023
    131.95    "Analytic"       0.048       -0.024    0.024
    123.11    "Analytic"       0.052       -0.026    0.026
    114.87    "Analytic"       0.056       -0.028    0.028
    107.18    "Analytic"        0.06        -0.03     0.03
       100    "Analytic"       0.064       -0.032    0.032

Obtain the time domain wavelets from the filter bank and plot their magnitudes. Use the table to set the minimum and maximum limits of the x-axis to the smallest Begin value and largest End value, respectively.

[psi,t] = wavelets(fb);
plot(t,abs(psi))
grid on
xlim([spsi.Begin(end) spsi.End(end)])
xlabel('Time (sec)')
ylabel('Magnitude')
title('Time Domain Wavelets')

Input Arguments

fb — Continuous wavelet transform filter bank

cwtfilterbank object

Continuous wavelet transform (CWT) filter bank, specified as a cwtfilterbank object.

thresh — Time support threshold

10e–4 (default) | positive real number

Time support threshold for the wavelet, specified as a positive real number between 0 and 0.05. The time support of the wavelet is defined as the first instant the integrated energy of the wavelet exceeds thresh and the last instant the integrated energy is less than 1−thresh.

Data Types: double

Output Arguments

spsi — Wavelet time supports

table

Wavelet time supports, returned as an Ns-by-5 MATLAB table, where Ns is the number of wavelet bandpass frequencies (equal to the number of scales). The table has five variables:

CF — Wavelet center frequency

positive real number

Wavelet center frequency, returned as a positive real number.

Data Types: double

IsAnalytic — Wavelet designation

"Analytic" | "Nonanalytic"

Wavelet designation, returned as a string. Wavelets that do not decay to 5% of their peak value at the Nyquist frequency are not considered analytic. The time support information for those wavelets are returned as NaNs.

Data Types: string

TimeSupport — Wavelet time support

positive integer | NaN

Wavelet time support, returned in samples, seconds, or MATLAB durations. The units of TimeSupport depend on whether you specify SamplingFrequency or SamplingPeriod. If you specify a SamplingFrequency, the units are seconds. If you specify a SamplingPeriod, the units are the same as the SamplingPeriod. If no SamplingFrequency or SamplingPeriod is specified, the units are samples.

Data Types: double

Begin — Beginning of wavelet time support

integer

Beginning of wavelet time support, returned as an integer. Begin is defined as the first instant the wavelet integrated energy exceeds the default threshold, 10⁻⁴. Begin has the same units as TimeSupport.

Data Types: double

End — End of wavelet time support

integer

End of wavelet time support, returned as an integer. End is defined as the last instant the wavelet integrated energy is less than 1 − 10⁻⁴. End has the same units as TimeSupport.

Data Types: double

Data Types: table

Version History

Introduced in R2018a