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(
,
the scaling function 'wname'
,ITER)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(
computes
and also plots the functions.'wname'
,ITER,'plot')
[S,W1,W2,W3,XYVAL] = wavefun2(
,
where wname
,A,B)A
and B
are positive integers,
is equivalent to [S,W1,W2,W3,XYVAL] = wavefun2(
.
The resulting functions are plotted. 'wname'
,max(A,B))
When A
is set equal to the special value
0,
[S,W1,W2,W3,XYVAL] = wavefun2(
is
equivalent to 'wname'
,0)[S,W1,W2,W3,XYVAL] = wavefun2(
.'wname'
,4,0)
[S,W1,W2,W3,XYVAL] = wavefun2(
is
equivalent to 'wname'
)[S,W1,W2,W3,XYVAL] = wavefun2(
.'wname'
,4)
The output arguments are optional.
Note
The |
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);
Daubechies, I., Ten lectures on wavelets, CBMS, SIAM, 1992, pp. 202Äì213.
Strang, G.; T. Nguyen (1996), Wavelets and Filter Banks, Wellesley-Cambridge Press.