| Group: | Mathematical Functions |
| Topic: | Fourier and Wavelet transforms |
| See also: | invfwtin dwt invdwt fwt invfwt fwtinshift |
| Function: | fwtin | |
| Description: | fwtin computes the Fast Wavelet Transformation of all circular shifts of the vector x. |
| Usage: | ti = fwtin (x, d, h) | |
| Input: | ||
| x | n x 1 vector, the input data, where n has to be a power of 2 | |
| d | integer, the level for the father wavelets s.t. 2^d is the number of father wavelet coefficients | |
| h | m x 1 vector, wavelet basis | |
| Output: | ||
| ti | n x d matrix, the resulting coefficients | |
To get the vectors of the wavelet basis, the library wavelet has to be loaded. h can be daubechies2,4,6,8,10,12,14,16,18,20, symmlet4 to 10 or coiflet1 to 5.
; set random seed of random generator
randomize(0)
; load the library wavelet to get the constants
library("wavelet")
; generate a x
x =(0:15)/16
; use as y a noisy sine curve
y = sin(pi*x)+normal(16)
; compute translation invariant coefficients
ti = fwtin(y, 2, daubechies4)
; show them on the screen
ti
Contents of ti [ 1,] -0.16276 0.1688 [ 2,] 0.13875 2.5233 [ 3,] 1.125 -1.4808 [ 4,] -0.22687 0.4851 [ 5,] 0.94395 0.10797 [ 6,] -0.61274 -1.8444 [ 7,] -0.26754 -0.36924 [ 8,] 0.22756 -0.44845 [ 9,] -0.4672 0.50097 [10,] 1.4851 -1.8111 [11,] -0.69653 -0.69367 [12,] 0.95768 1.2814 [13,] 0.79618 -1.169 [14,] -0.60832 1.6624 [15,] -0.19415 0.7346