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MakeWavelet

Make periodized orthogonal wavelet

Calling Sequence

wave = MakeWavelet(j,k [,Family,par,Gender,n])

Parameters

Inputs:

j,k :

location-scale indices: 2^{-j} approx width of wavelet k/2^j approx loc'n of wavelet on unit interval

Family :

string: 'Haar', 'Daubechies', 'Coiflet', 'Symmlet', 'Interpolating', 'AverageInterpolating', 'Meyer', 'Battle' Default: 'Symmlet', Nearly-Symmetric ON Wavelet

par :

integer parameter to MakeONFilter, MakeDDFilter. When Default 'Symmlet' active, default 8.

Gender :

'Mother', 'Father'

n :

signal length (dyadic)

Outputs:

wave :

1-d signal, the wavelet

Description

The Haar filter (which could be considered a Daubechies-2) was the first wavelet, though not called as such, and is discontinuous.

The Coiflet filters are designed to give both the mother and father wavelets 2*Par vanishing moments; here Par may be one of 1,2,3,4 or 5.

The Daubechies filters are minimal phase filters that generate wavelets which have a minimal support for a given number of vanishing moments. They are indexed by their length, Par, which may be one of 4,6,8,10,12,14,16,18 or 20. The number of vanishing moments is par/2.

Symmlets are also wavelets within a minimum size support for a given number of vanishing moments, but they are as symmetrical as possible, as opposed to the Daubechies filters which are highly asymmetrical. They are indexed by Par, which specifies the number of vanishing moments and is equal to half the size of the support. It ranges from 4 to 10.

The Battle-Lemarie filter generate spline orthogonal wavelet basis. The parameter Par gives the degree of the spline. The number of vanishing moments is Par+1.

The Meyer wavelet has an infinite number of vanishing moments. The time decay depends upon the regularity of the spectral window used to build it. In this case, these windows are built with polynomials whose degree are given by the parameter Par.

The Interpolating wavelets are Dubuc-Deslauriers wavelets which are interpolating functions that can reproduce polynomials of degree equal to Par.

Authors

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