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Wavelet and scaling functions 2-D



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.


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


See wavefun for more information.

See Also
intwave, wavefun, waveinfo, wfilters


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

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

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