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cwttrack(2) Scilab Function cwttrack(2)
NAME
cwttrack - Continuous L2 wavelet based Holder exponent estimation
Author: Paulo Goncalves
Estimates the local or global Holder exponent of a 1-D signal from its L2
continuous wavelet transform ( output of contwt(mir) ). In some cases, the
global Holder exponent can also be refered to as the long range dependance
parameter
Usage
[HofT] = cwttrack(wt,scale,whichT,FindMax,ChooseReg,radius,DeepScale,Show)
Input parameters
o wt : Real or complex matrix [N_scale,N] Wavelet coefficients of a
continuous wavelet transform (output of contwt)
o scale : real vector [1,N_scale] Analyzed scale vector
o whichT : Integer whichT, when non zero specifies the time position
on the signal where to estimate the local Holder exponent. When
whichT is zero, the global scaling exponent (or LRD exponent) is
estimated.
o FindMax : 0/1 flag. FindMax = 0 : estimates the Holder exponents
(local or global) from all coefficients of the wavelet transform
FindMax = 1 : estimates the Holder exponents (local or global) from
the local Maxima coefficients of the wavelet transform Default value
is FindMax = 1
o ChooseReg : 0/1 flag or integer vector [1,N_reg], (N_reg <= N_scale)
ChooseReg = 0 : full scale range regression ChooseReg = 1 : scale
range is choosed by the user, clicking with the mouse on a regres-
sion graph. ChooseReg = [n1 ... nN_reg] : imposes the scale indices
for the linear regression of the wavelet coefficients versus scale
in a log-log plot Default value is ChooseReg = 0
o radius : Positive integer. The local maxima line search is res-
tricted to some neighbourhood of the analyzed point. Basically, this
region is defined by the cone of influence of the wavelet. radius
allows to modulate the width of the cone. Default value is cone =
8 .
o DeepScale : strictly positive integer. DeepScale tells the maxima
line procedure how depth in scale to scan from step to step. Default
value is DeepScale = 1
o Show 0/1 flag.
Show = 1 : display the maxima line trajectory and the log-log
regression graph
Show = 0 : no display
Output parameters
o HofT : Real scalar. Local or global Holder exponent estimated
Algorithm details
The maxima line search follows the two steps:
o all local maxima are found using a standard gradient technique
o local maxima are connected along scales by finding the minimum
Lobatchevsky distance between two consecutive maxima lying beneath
the cone of influence.
See also:
cwttrack_all, contwtspec, contwt, dwtspec
Example:
N = 1024 ;
[x] = GeneWei(N,[ones(1,N/2)*0.2 ones(1,N/2)*0.8],2,1,1) ;
[wt,scale] = contwtmir(x,2^(-8),2^(-1),64,8*i) ;
HofT_1 = cwttrack(wt,scale,N/4,1,1)
HofT_2 = cwttrack(wt,scale,3*N/4,1,1)
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