Wavelet Toolbox
wavefun2

Wavelet and scaling functions 2-D

Syntax

• ```[S,W1,W2,W3,XYVAL] = wavefun2('`wname`',ITER)
[S,W1,W2,W3,XYVAL] = wavefun2('`wname`',ITER,'plot')
[S,W1,W2,W3,XYVAL] = wavefun2('`wname`',A,B)
```

Description

For an orthogonal wavelet `'``wname``'`, ` wavefun2` returns the scaling function and the three wavelet functions resulting from the tensor products of the one-dimensional scaling and wavelet functions.

If `[PHI,PSI,XVAL] = wavefun('``wname``',ITER)`, the scaling function `S` is the tensor product of `PHI` and `PSI`.

The wavelet functions `W1`, `W2` and `W3` are the tensor products (`PHI`,`PSI`), (`PSI`,`PHI`) and (`PSI`,`PSI`), respectively.

The two-dimensional variable `XYVAL` is a 2ITER x 2ITER points grid obtained from the tensor product (`XVAL`,`XVAL`).

The positive integer `ITER` determines the number of iterations computed and thus, the refinement of the approximations.

[S,W1,W2,W3,XYVAL] = wavefun2('`wname`',ITER,'plot') computes and also plots the functions.

[S,W1,W2,W3,XYVAL] = `wavefun2('``wname``',A,B)`, where `A` and `B` are positive integers, is equivalent to
[S,W1,W2,W3,XYVAL] = `wavefun2('``wname``',max(A,B))`. The resulting functions are plotted.

When `A` is set equal to the special value 0,

[S,W1,W2,W3,XYVAL] = `wavefun2('``wname``',0)` is equivalent to [S,W1,W2,W3,XYVAL] = `wavefun2('``wname``',4,0)`.

[S,W1,W2,W3,XYVAL] = `wavefun2('``wname``')` is equivalent to [S,W1,W2,W3,XYVAL] = `wavefun2('``wname``',4)`.

The output arguments are optional.

 Note    The `wavefun2 `function can only be used with an orthogonal wavelet.

Examples

On the following graph, a linear approximation of the `sym4` wavelet obtained using the cascade algorithm is shown.

• ```% Set number of iterations and wavelet name.
iter = 4;
wav = 'sym4';

% Compute approximations of the wavelet and scale functions using
% the cascade algorithm and plot.
[s,w1,w2,w3,xyval] = wavefun2(wav,iter,0);

```

Algorithm

See `wavefun` for more information.

```intwave, wavefun, waveinfo, wfilters ```