# waveletsupport

CWT filter bank time supports

## Description

## 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 `NaN`

s.

**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**

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