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. |
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 |
The matrix b contains in the first two columns the indices of the coefficient of the mother wavelet and in the third column the coefficient itself. The results for the coefficients differ from dwt by the factor 1/sqrt(n).
library("wavelet") x =(0:1023)/1023 {a, b} = fwt(x, 4, daubechies4) a b
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