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# waveletsupport

DWT filter bank time supports

## Syntax

``spsi = waveletsupport(fb)``
``spsi = waveletsupport(fb,thresh)``
``[spsi,sphi] = waveletsupport(fb)``
``[spsi,sphi,tlow,thigh] = waveletsupport(fb)``

## Description

example

````spsi = waveletsupport(fb)` returns the wavelet time supports of the discrete wavelet transform (DWT) filter bank `fb`. The time supports are defined as the time interval in which all the wavelet energy occurs (> 99.99% of the energy for the default threshold).```
````spsi = waveletsupport(fb,thresh)` specifies the threshold for the integrated energy. `thresh` is a positive real number in the interval 0 < `thresh` ≤ 0.05.```
````[spsi,sphi] = waveletsupport(fb)` returns the scaling function time supports at all levels. `sphi` is a real-valued L-by-1 vector, where L is the number of levels in the DWT filter bank `fb`.```
````[spsi,sphi,tlow,thigh] = waveletsupport(fb)` returns the instants the integrated energy in the wavelets and scaling functions exceed `thresh` in `tlow` and the last instant the integrated energy is less than 1 − `thresh` in `thigh`.```

## Examples

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Find the time supports for a Haar wavelet filter bank.

```fb = dwtfilterbank('Wavelet','haar','Level',8); Spsi = waveletsupport(fb)```
```Spsi = 8×1 2 4 8 16 32 64 128 256 ```

## Input Arguments

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Discrete wavelet transform (DWT) filter bank, specified as a `dwtfilterbank` object.

Threshold for the integrated energy, specified as a positive scalar in the interval 0 < `thresh` ≤ 0.05. If unspecified, `thresh` defaults to 10-6.

The percent energy contained in the time support is (1 − 2 × `thresh`) × 100. The time support of the wavelet is defined as the first instant the integrated energy exceeds `thresh` and the last instant it is less than 1-`thresh`. The wavelets are normalized to have unit energy for the computation.

## Output Arguments

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Wavelet time supports, returned as a real-valued column vector of length L, where L is the number of levels in the DWT filter bank.

Scaling function time supports, returned as a real-valued column vector of length L, where L is the number of levels in the DWT filter bank.

First instants the integrated energy in the wavelet and scaling functions exceed `thresh`, returned as real-valued L-by-2 matrix, where L is the number of levels in the filter bank. The first column of `tlow` contains the times for the wavelets. The second column of `tlow` contains the times for the scaling functions.

The difference between the first column of `thigh` and the first column of `tlow` plus one sampling period equals `pspi`. The difference between the second column of `thigh` and the second column of `tlow` plus one sampling period equals `sphi`.

Last instants the integrated energy in the wavelet and scaling functions is less than 1−`thresh`, returned as real-valued L-by-2 matrix, where L is the number of levels in the filter bank. The first column of `thigh` contains the times for the wavelets. The second column of `thigh` contains the times for the scaling functions.

The difference between the first column of `thigh` and the first column of `tlow` plus one sampling period equals `pspi`. The difference between the second column of `thigh` and the second column of `tlow` plus one sampling period equals `sphi`.

## Version History

Introduced in R2018a