MakeONFilter -- Generate Orthonormal QMF Filter for Wavelet Transform

Usage

qmf = MakeONFilter(Type,Par)

Inputs

Type

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

Par

integer, e.g. if Type = 'Coiflet', Par=3 specifies a Coiflet-3 wavelet

Outputs

qmf quadrature mirror filter

Description

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

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 maximize the smoothness of the father wavelet (or "scaling function") by maximizing the rate of decay of its Fourier transform. They are indexed by their length, Par, which may be one of 4,6,8,10,12,14,16,18 or 20.

Symmlets are the "least asymmetric" compactly-supported wavelets with maximum number of vanishing moments, here indexed by Par, which 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.

See Also

FWT_PO, IWT_PO, FWT2_PO, IWT2_PO, WPAnalysis

References

The books by Daubechies and Wickerhauser.