Wavelet Toolbox™

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 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('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.

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.

See Also
intwave, wavefun, waveinfo, wfilters

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