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

Library: wavelet
See also: fwt invfwt fwt2 invfwt2 fwttin

Quantlet: wavesmo
Description: Generates smoothed mother wavelet coeffients and the resulting estimate. x contains the vector of data and l gives the number of father wavelet coefficient (power of 2). h is the vector of wavelet basis coeffients (automatically generated by calling the quantlib wavelet). s contains the threshold values, either one for all mother wavelet coefficients or for each level. Set tt=0 for hard thresholding and tt=1 for soft thresholding.

Link:
Usage: {a, b, xs} = wavesmo (x, l, h, s, tt)
Input:
x n x 1 array (n has to be a power of 2), input data, observed at an equispaced grid
l p x 1 array, giving the number of father wavelets
h q x 1 array, wavelet basis coefficients
s r x 1 array, binwidth
tt scalar, 0=hard, 1=soft thresholding
Output:
a l x 1 array, father wavelet coefficients
b n-l x 1 array, mother wavelet coefficients
xs n x 1 array, smoothed estimate of x

Example:

; loads the library wavelet

library ("wavelet")

; generates an equidistant grid from 0 to 1.5 with

; binwidth 0.1 

x = grid(0, 0.1, 16)

; computes z_i = x_i *x_i

z = x^2

; chooses the number father wavelet as one

l = 1

; computes the thresholded coefficients and

; the thresholded data

{a, b, xs} = wavesmo (z, l, haar, 0.1, 0)

a

b

xs 

Result:

Unthresholded father wavelet coeffients a and thresholded

mother wavelet coefficients b and smoothed estimate xs 


Library: wavelet
See also: fwt invfwt fwt2 invfwt2 fwttin

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

Author: Sigbert Klinke, 960618, Sperlich 980105
(C) MD*TECH Method and Data Technologies, 21.9.2000