# wavelets

CWT filter bank time-domain wavelets

## Syntax

``psi = wavelets(fb)``
``[psi,t] = wavelets(fb)``

## Description

````psi = wavelets(fb)` returns the time-domain wavelets `psi` for the continuous wavelet transform (CWT) filter bank `fb`. The time-domain wavelets are centered at the origin.```

example

````[psi,t] = wavelets(fb)` returns the sampling instants `t` for the wavelets.```

## Examples

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Create a continuous wavelet transform filter bank. Set the sampling frequency to 1000 Hz and the frequency limits to range from 50 Hz to 200 Hz. Plot the frequency response.

```fb = cwtfilterbank('SamplingFrequency',1000,'FrequencyLimits',[50 200]); freqz(fb)```

Obtain the filter bank time-domain wavelets. Plot the magnitudes of the first and last wavelets contained in the output. The first wavelet corresponds to the wavelet filter with center frequency equal to 200 Hz, and the last wavelet corresponds to the wavelet filter with center frequency equal to 50 Hz.

```[psi,t] = wavelets(fb); figure plot(t,abs(psi(1,:))) hold on plot(t,abs(psi(end,:))) legend('Higher CF Wavelet','Lower CF Wavelet') grid on```

## Input Arguments

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

## Output Arguments

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Time-domain wavelets, returned as a Ns-by-N complex-valued matrix, where Ns is the number of wavelet bandpass frequencies (equal to the number of scales) and N is the filter bank `SignalLength`. The wavelets are ordered in `psi` from the highest-frequency passband filter to the lowest-frequency passband filter.

Sampling instants of the time-domain wavelets, returned as a real-valued vector of length N, where N is the filter bank `SignalLength`. The data type of `t` is the same as the `SamplingPeriod`.

## Version History

Introduced in R2018a