bswfun
Biorthogonal scaling and wavelet functions
Syntax
[PHIS,PSIS,PHIA,PSIA,XVAL] = bswfun(LoD,HiD,LoR,HiR)
bswfun(LoD,HiD,LoR,HiR,ITER)
bswfun(LoD,HiD,LoR,HiR,'plot')
bswfun(LoD,HiD,LoR,HiR,ITER,'plot')
bswfun(LoD,HiD,LoR,HiR,'plot',ITER)
Description
[PHIS,PSIS,PHIA,PSIA,XVAL] = bswfun(LoD,HiD,LoR,HiR) returns
approximations on the grid XVAL of the two pairs
of biorthogonal scaling and wavelet functions. PHIS and PSIS are
the scaling and wavelet functions constructed from the decomposition
filters, LoD and HiD. PHIA and PSIA are
the scaling and wavelet functions constructed from the reconstruction
filters, LoR and HiR.
bswfun(LoD,HiD,LoR,HiR,ITER) computes the
two pairs of scaling and wavelet functions using ITER iterations.
bswfun(LoD,HiD,LoR,HiR,'plot') or bswfun(LoD,HiD,LoR,HiR,ITER,'plot') or bswfun(LoD,HiD,LoR,HiR,'plot',ITER) computes
and plots the functions.
Examples
Biorthogonal Scaling and Wavelet from Lifting Scheme
This example shows how to obtain the biorthogonal scaling and wavelet functions corresponding to a lifting scheme. Obtain the lifting scheme for the CDF 3/1 wavelet.
lscdf = liftwave('cdf3.1');Display the lifting scheme, which consists of two primal and one dual step.
Sc = displs(lscdf); Sc
Sc = 6x50 char array
'lscdf = {... '
''p' [ -0.33333333] [-1] '
''d' [ -0.37500000 -1.12500000] [1] '
''p' [ 0.44444444] [0] '
'[ 2.12132034] [ 0.47140452] [] '
'}; '
Obtain the decomposition and reconstruction filters from the lifting scheme.
[LoD,HiD,LoR,HiR] = ls2filt(lscdf);
Visualize the scaling and wavelet function and their duals.
bswfun(LoD,HiD,LoR,HiR,'plot');
Algorithms
This function uses the cascade algorithm.