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waveletsupport

DWT filter bank time supports

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.

Introduced in R2018a