This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English version of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materials including this page, select Japan from the country navigator on the bottom of this page.


Wavelet and scaling functions 2-D


[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)


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.


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


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);


See wavefun for more information.


Daubechies, I., Ten lectures on wavelets, CBMS, SIAM, 1992, pp. 202Äì213.

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

Introduced before R2006a

Was this topic helpful?