MakeONFilter {rwavelet}

Generate Orthonormal QMF Filter for Wavelet Transform

Description

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

Usage

MakeONFilter(Type, Par)

Arguments

Type

string, 'Haar', 'Beylkin', 'Coiflet', 'Daubechies' 'Symmlet', 'Vaidyanathan','Battle'.

Par

integer, it is a parameter related to the support and vanishing moments of the wavelets, explained below for each wavelet.

Details

The Beylkin filter places roots for the frequency response function close to the Nyquist frequency on the real axis.

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 Vaidyanathan filter gives an exact reconstruction, but does not satisfy any moment condition. The filter has been optimized for speech coding.

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.

Value

qmf quadrature mirror filter.

See Also

FWT_PO, IWT_PO, FWT2_PO, IWT2_PO.

Examples

Type <- 'Coiflet'
Par <- 1
qmf <- MakeONFilter(Type, Par)