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: 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

Note:
In density or regression estimation the input data have to be realizations on an equispaced grid.

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.

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)
; show them on the screen
ti

```
Result:
```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
```

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