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