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: fwtin fwt invfwt dwt invdwt fwtinshift

Function: invfwtin
Description: fwtin computes the inverse Fast Wavelet Transformation of all circular shifts from ti.

Link:
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

Note:

Example:



; 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 

Result:



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


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

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

(C) MD*TECH Method and Data Technologies, 21.9.2000