intwave

Integrate wavelet function psi (ψ)

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 2^prec points grid xval.

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

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

Examples

Integrate Approximation of Wavelet Function

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"]);

Input Arguments

wname — Wavelet

character vector | string scalar

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

Data Types: char | string

prec — Number of iterations

8 (default) | positive integer

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

in2,in3 — Number of iterations

pair of positive integers

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

integ — Integral

vector

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.

xval — Grid points

real-valued vector

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

intdec — Integral

vector

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

intrec — Integral

vector

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

Algorithms

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

Version History

Introduced before R2006a