| 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. |
| 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 | |
; 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
Unthresholded father wavelet coeffients a and thresholded mother wavelet coefficients b and smoothed estimate xs