Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

 Group: Mathematical Functions Topic: Fourier and Wavelet transforms See also: invfwt2 fwt invfwt dwt invdwt fwtin fwtinshift

 Function: fwt2 Description: fwt2 is designed for 2-dimensional wavelet transformation. It corresponds mainly to dwt for the one-dimensional case. If needed it can work with the tensor product of one dimensional wavelet transforms.

 Usage: c = fwt2 (x, l, h, a) Input: x n x n matrix, input data where n has to be a power of 2 l integer, l^2 is the number of the father wavelet coefficients h m x 1 vector, wavelet basis a integer, 0,1,2,3,... see notes Output: c n x n matrix, resulting coefficients

Note:
In density or regression estimation the input data have to be realizations on an equispaced grid. The parameter a indicates symmetry properties of 2 dimensional wavelet transform. The case a = 0 corresponds to the classical 2 dimensional wavelet transformation. The case a >= log_2(n) gives the tensor product of one dimensional wavelet transforms.

To get vectors of the wavelet basis, the library wavelet has to be loaded: h can be either daubechies2,4,6,8,10,12,14,16,18,20, symmlet4 to 10 or coiflet1 to 5.

Example:
```; loads the wavelet library
library("wavelet")
; initializes random generator
randomize(0)
; generates some data(line from top left to bottom right)
n = 16
i = 1:n
xo =(i.=i')
x  = xo+0.2.*normal(n,n)
; computes bivariate wavelet coefficients
c = fwt2(x, 4, daubechies4, 0);
; hard threshold
c = c.*(abs(c).>0.3)
; applies inverse transformation
y = invfwt2(c, 4, daubechies4, 0)
; compares orginal picture with thresholded picture
max(max(abs(y-xo),2))

```
Result:
```Content of max

[1,]  0.48421
```

(C) MD*TECH Method and Data Technologies, 05.02.2006