intwave

Integrate wavelet function psi (ψ)

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    Syntax

    [integ,xval] = intwave(wname)
    [integ,xval] = intwave(wname,prec)
    [intdec,xval,intrec] = intwave(wname,prec)
    [integ,xval] = intwave(wname,in2,in3)

    Description

    [integ,xval] = intwave(wname) computes the integral, integ, of the wavelet function ψ specified by wname. The function ψ is approximated on the 28 points grid xval.

    [integ,xval] = intwave(wname,prec) approximates the wavelet function on the 2prec points grid xval.

    example

    [intdec,xval,intrec] = intwave(wname,prec) computes the integrals, intdec and intrec, of the wavelet decomposition function ψdec and the wavelet reconstruction function ψrec, respectively. This syntax is valid only for biorthogonal wavelets.

    [integ,xval] = intwave(wname,in2,in3) approximates the function ψ is on the 2max(in2,in3) points grid xval and plots the results.

    Examples

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    Open Live Script

    Specify a wavelet name.

    wname = "db4";

    Use wavefun to obtain the wavelet function. Specify seven iterations.

    iter = 7;
[~,psi,xval] = wavefun(wname,iter);

    Compute the integrals of the wavelet approximation.

    [integ,~] = intwave(wname,iter);

    Plot the results.

    tiledlayout(2,1)
nexttile
plot(xval,psi)
title("Wavelet")
nexttile
plot(xval,integ)
title(["Wavelet Integrals Over [-Inf x] " ... 
       "For Each Value of xval"]);

    Figure contains 2 axes objects. Axes object 1 with title Wavelet contains an object of type line. Axes object 2 with title Wavelet Integrals Over [-Inf x] For Each Value of xval contains an object of type line.

    Input Arguments

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    Wavelet, specified as a character vector or string scalar. For more information, see waveinfo and wfilters.

    Data Types: char | string

    Number of iterations used to approximate the wavelet function, specified as a positive integer.

    For the special value 0, intwave(wname,0) is equivalent to intwave(wname,8).

    Data Types: double

    Number of iterations used to approximate the wavelet function, specified as a pair of positive integers. The number of iterations is equal to max(in2,in3).

    For the special value 0, intwave(wname,0,in3) is equivalent to intwave(wname,8,in3).

    Data Types: double

    Output Arguments

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    Integral of the wavelet function ψ, returned as a vector. The intwave function computes the integral of ψ (from −∞ to xval values): , for x in xval.

    integ is a real- or complex valued vector, depending on the wavelet type.

    Grid points where the wavelet function approximation is evaluated, returned as a real-valued vector.

    Integral of the biorthogonal wavelet decomposition function ψdec, returned as a vector.

    Integral of the biorthogonal wavelet reconstruction function ψrec, returned as a vector.

    Algorithms

    First, the wavelet function is approximated on a grid of 2prec points using wavefun. A piecewise constant interpolation is used to compute the integrals using cumsum.

    Version History

    Introduced before R2006a

    See Also