Wavelet Toolbox |

Wavelet and scaling functions 2-D

**Syntax **

[S,W1,W2,W3,XYVAL] = wavefun2('

',ITER) [S,W1,W2,W3,XYVAL] = wavefun2('*wname*

',ITER,'plot') [S,W1,W2,W3,XYVAL] = wavefun2('*wname*

',A,B)*wname*

**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 2^{ITER} x 2^{ITER} 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('

',ITER,'plot') computes and also plots the functions.*wname*

[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.

**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.

**See Also**

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

**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.

wavefun | waveinfo |