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bswfun

Biorthogonal scaling and wavelet functions

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    Syntax

    [phis,psis,phia,psia,xval] = bswfun(lod,hid,lor,hir)
    [___] = bswfun(___,iter)
    [___] = bswfun(___,"plot")

    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 (lod,hid) and (lor,hir), using the two pairs of filters (lod,hid) and (lor,hir).

    [___] = bswfun(___,iter) computes the two pairs of scaling and wavelet functions using iter iterations.

    [___] = bswfun(___,"plot") also plots the functions.

    bswfun(lod,hid,lor,hir,"plot",iter) is equivalent to bswfun(lod,hid,lor,hir,iter,"plot").

    example

    Examples

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    Open Live Script

    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 = liftingScheme(Wavelet="cdf3.1");

    Display the lifting scheme.

    disp(lscdf)
     	 Wavelet               : 'cdf3.1' 
	 LiftingSteps          : [3 × 1] liftingStep 
	 NormalizationFactors  : [2.1213 0.4714] 
	 CustomLowpassFilter   : [  ] 


 Details of LiftingSteps :
            Type: 'update'
    Coefficients: -0.3333
        MaxOrder: -1

            Type: 'predict'
    Coefficients: [-0.3750 -1.1250]
        MaxOrder: 1

            Type: 'update'
    Coefficients: 0.4444
        MaxOrder: 0

    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");

    Figure contains 4 axes objects. Axes object 1 with title Analysis scaling function (phiA) contains an object of type line. Axes object 2 with title Analysis wavelet function (psiA) contains an object of type line. Axes object 3 with title Synthesis scaling function (phiS) contains an object of type line. Axes object 4 with title Synthesis wavelet function (psiS) contains an object of type line.

    Input Arguments

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    Decomposition filters, specified as a pair of vectors. lod is the lowpass decomposition filter, and hid is the highpass decomposition filter.

    Data Types: double

    Reconstruction filters, specified as a pair of vectors. lor is the lowpass reconstruction filter, and hir is the highpass reconstruction filter.

    Data Types: double

    Number of iterations used to generate the wavelet and scaling functions, specified as a positive integer. Larger values of iter increase the refinement of the approximations.

    Output Arguments

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    Biorthogonal scaling and wavelet functions constructed from the decomposition filter pair (lod,hid), returned as vectors. phis is the approximation of the scaling function and psis is the approximation of the wavelet function.

    Biorthogonal scaling and wavelet functions constructed from the reconstruction filter pair (lor,hir), returned as vectors. phia is the approximation of the scaling function and psia is the approximation of the wavelet function.

    Grid points where the approximations are evaluated, returned as a vector.

    Algorithms

    This function uses the cascade algorithm.

    Version History

    Introduced before R2006a

    See Also