# wavefun2

Wavelet and scaling functions 2-D

## Syntax

```[PHI,PSI,XVAL] = wavefun('wname',ITER) [S,W1,W2,W3,XYVAL] = wavefun2('wname',ITER,'plot') [S,W1,W2,W3,XYVAL] = wavefun2(wname,A,B) [S,W1,W2,W3,XYVAL] = wavefun2('wname',max(A,B)) [S,W1,W2,W3,XYVAL] = wavefun2('wname',0) [S,W1,W2,W3,XYVAL] = wavefun2('wname',4,0) [S,W1,W2,W3,XYVAL] = wavefun2('wname') [S,W1,W2,W3,XYVAL] = wavefun2('wname',4) ```

## 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); ``` ## Algorithms

See `wavefun` for more information.

## References

Daubechies, I., Ten lectures on wavelets, CBMS, SIAM, 1992, pp. 202–213.

Strang, G.; T. Nguyen (1996), Wavelets and Filter Banks, Wellesley-Cambridge Press. 