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: invfwt dwt invdwt fwtin fwtinshift fwt2

Function: fwt
Description: fwt computes the Fast Wavelet Transformation of a vector.

Link:
Usage: {a, b} = fwt (x, l, h)
Input:
x n x 1 vector, input data where n has to be a power of 2
l integer, number of father wavelet coefficients
h m x 1 vector, wavelet basis
Output:
a l x 2 matrix, indices and coefficients of the father wavelets
b (n-l) x 3 matrix, indices and coefficients of the mother wavelets

Note:

Example:
library("wavelet")
x =(0:1023)/1023
{a, b} = fwt(x, 4, daubechies4)
a
b

Result:
Contents of a

[1,]        0  0.079014
[2,]        1  0.20414
[3,]        2  0.33734
[4,]        3   0.3795
Contents of b

[   1,]        1        0 -0.11404
[   2,]        1        1 -4.9204e-17
[   3,]        1        2 -3.5032e-17
[   4,]        1        3  0.030175
[   5,]        2        0 -0.080708
[   6,]        2        1 -1.5787e-17
[   7,]        2        2 -1.2105e-17
[   8,]        2        3 -3.6657e-17

...

[ 676,]        8      167 -1.2086e-18
[ 677,]        8      168 -1.1804e-18
[ 678,]        8      169 -1.369e-18
[ 679,]        8      170 -9.0717e-19
[ 680,]        8      171 -1.0957e-18
[ 681,]        8      172 -1.2844e-18
[ 682,]        8      173 -8.2247e-19
[ 683,]        8      174



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