MakeONFilter -- Generate Orthonormal QMF Filter for Wavelet Transform
Usage
qmf = MakeONFilter(Type,Par)
Inputs
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.
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 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.
See Also
FWT_PO, IWT_PO, FWT2_PO, IWT2_PO, WPAnalysis
References
The books by Daubechies and Wickerhauser.