.Wavelet.Families

Information

This section defines all available wavelets in this library. Since different wavelets have different properties, the functions for different wavelets require different input parameters and generate different output data. All available wavelets in this library with the parameters are listed in the following table.

Parameter, Nd, specifies the wavelet order. Nr is only used for biorthogonal wavelets, where Nd is for decomposition and Nr for reconstruction.

For the wavelets with theoretically unlimited support, e.g. Meyer, Gaussian, etc., the function range is set as effective support, [-es, es], if 'range' is not specified (==0).

Parameters, fb and fc, are used for some complex wavelets. These are the so-called frequency parameters defining the oscillation properties of the wavelets.

'phi' stands for scaling function, and 'psi' for wavelet function. A biorthogonal wavelet has two scaling and wavelet functions. The first function set is for forward transformation (decomposition); the second set is for inverse transformation (reconstruction).

Symbol, O, means the corresponding parameter is applicable, - not applicable, for a specific wavelet.

For generating Meyer wavelets, an external C-function saved in fft_c.c file has to be called. This C-file has to be available in the current working directory or the searching path of Modelica must include the directory of fft_c.c file.

Applicable parameters of the wavelet families

Wavelet wavID wavType Nd Nr es range fb fc phi1 psi1 phi2 psi2
Haar 1 1 - - - - - - O O - -
Daubechies 2 1 1..20 - - - - - O O - -
Symlets 3 1 1..20 - - - - - O O - -
Coiflets 4 1 1..5 - - - - - O O - -
Biorthogonal spline 5 2 1..6 1..9 - - - - O O O O
Reverse biorthogonal spline 6 2 1..9 1..6 - - - - O O O O
Discrete Meyer 7 3 - - 8 >=0 - - O O - -
Meyer 8 3 - - 8 >=0 - - O O - -
Gaussian 9 4 1..8 - 5 >=0 - - - O - -
Mexican hat 10 4 - - 5 >=0 - - - O - -
Morlet 11 4 - - 4 >=0 - - - O - -
Complex Gaussian 12 5 1..8 - 5 >=0 - - - O - -
Complex Morlet 13 5 - - 4 >=0 >0 >0 - O - -
Complex Shannon 14 5 - - 20 >=0 >0 >0 - O - -
Complex frequency B-spline 15 5 1,2,... - 20 >=0 >0 >0 - O - -

Available orders for biorthogonal and reverse biorthogonal wavelets

For biorthogonal and reverse biorthogonal wavelets, only some combinations of the orders are available. For details, refer to the functions, wavBiorSpline and wavRevBiorSpline.

Wavelet types

All wavelets are categorized into five types. They are defined as follows:

Type Description
1 Orthogonal wavelets
2 Biorthogonal wavelets
3 Non-(bi)orthogonal wavelets with scaling function
4 Non-(bi)orthogonal wavelets without scaling function
5 Complex wavelets (without scaling function)

Contents

Name Description
 wavFunc Returns the filter bank and functions of a specific wavelet family
 scalingWaveFunc Generate the scaling and wavelet functions using wavelet filters
 wavHaar Haar wavelet filters
 wavDaubechies Daubechies wavelet filters
 wavSymlets Symlets wavelet filters
 wavCoiflets Coiflets wavelet filters
 wavBiorSpline Biorthogonal spline wavelet filters
 wavRevBiorSpline Reverse biorthogonal spline wavelet filters
 wavDMeyer Discrete Meyer wavelet filters
 wavMeyer Meyer wavelet function. The fft_c.c file must be accessible.
 wavGaussian Gaussian wavelet function
 wavMexHat Mexican hat wavelet function
 wavMorlet Morlet wavelet function
 wavXGaussian Complex Gaussian wavelet function
 wavXMorlet Complex Morlet wavelet function
 wavXShannon Complex Shannon wavelet function
 wavXFreqBSpline Complex Frequency B-Spline wavelet

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