Documentation

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

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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 =

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');

More About

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Algorithms

This function uses the cascade algorithm.

See Also

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