| Group: | Mathematical Functions |
| Topic: | Fourier and Wavelet transforms |
| See also: | fwtin fwt invfwt dwt invdwt fwtinshift |
| Function: | invfwtin | |
| Description: | fwtin computes the inverse Fast Wavelet Transformation of all circular shifts from ti. |
| Usage: | x = invfwtin (ti, d, h) | |
| Input: | ||
| ti | n x d matrix, the wavelet coefficients of all circular shifts, can be retrieved by fwtin. 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: | ||
| x | n x 1 vector | |
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)
; make a small hardthresholding
ti = ti.*(abs(ti).>0.5)
; transform back to estimated data
yh = invfwtin(ti, 2, daubechies4)
; compare original and thresholded data
y~yh
Contents of _tmp [ 1,] -0.21293 -0.081272 [ 2,] -0.81271 -0.63678 [ 3,] 2.3329 2.2874 [ 4,] -0.74961 -0.81817 [ 5,] -0.72704 -0.7112 [ 6,] 1.5296 1.5929 [ 7,] 0.53442 0.39329 [ 8,] -0.59385 -0.36972 [ 9,] 0.73405 0.71432 [10,] 1.1803 1.1917 [11,] -1.5795 -1.6033 [12,] 0.33883 0.36711 [13,] -0.51739 -0.2067 [14,] 0.13434 0.0072323 [15,] -0.34705 -0.056144 [16,] 0.40373 0.32672