# wavefun2

Wavelet and scaling functions 2-D

## Description

[s,w1,w2,w3,xyval] = wavefun2(wname,iter) returns an approximation s of the 2-D scaling function and approximations w1, w2, and w3 of the three 2-D wavelet functions associated with the orthogonal wavelet wname. xyval is a 2-D grid of points. The positive integer iter specifies the number of iterations.

The approximations are the tensor products of the one-dimensional scaling and wavelet functions associated with the orthogonal wavelet wname. For more information, see Algorithms.

[s,w1,w2,w3,xyval] = wavefun2(wname,iter,'plot') also plots the functions.

example

[___] = wavefun2(wname,a,b) returns the approximations using max(a,b) iterations. The wavefun2 function also plots the approximations.

• wavefun2(wname,0) is equivalent to wavefun2(wname,4,0).

• wavefun2(wname) is equivalent to wavefun2(wname,4).

## Examples

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Specify an orthogonal wavelet.

wav = "sym4";

Obtain and plot the approximations of the 2-D scaling function and wavelets. Specify four iterations.

iter = 4;
[s,w1,w2,w3,xyval] = wavefun2(wav,iter,0);

Obtain the wavelet approximation corresponding to the $\left(\varphi ,\psi \right)$ tensor product using one iteration. Compare with the first approximation.

[~,w1x] = wavefun2(wav,1);
tiledlayout(1,2)
nexttile
imagesc(w1)
title("Four Iterations")
nexttile
imagesc(w1x)
title("One Iteration")

## Input Arguments

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Orthogonal wavelet, specified as a character vector or string scalar. For a list of orthogonal wavelets, see wfilters.

Data Types: char | string

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

Data Types: double

Iteration, specified as a pair of positive integers. The number of iterations is equal to max(a,b).

## Output Arguments

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2-D scaling function approximation, returned as a matrix. For more information, see Algorithms.

2-D wavelet function approximations, returned as matrices. For more information, see Algorithms.

## Algorithms

The wavefun2 function returns approximations of the 2-D scaling function and the three 2-D wavelet functions resulting from the tensor products of the one-dimensional scaling and wavelet functions associated with the orthogonal wavelet wname.

If [phi,psi,xval] = wavefun(wname,iter), then:

• s is the tensor product of phi and phi.

• w1, w2, and w are the tensor products (phi,psi), (psi,phi), and (psi,psi), respectively.

• xyval is the tensor product (xval,xval).