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.TH "cwtspec" 2 " June 6th 1997" "Fractales Group" "Scilab Function"
.so ../sci.an
.SH NAME
cwtspec - Continuous L1 wavelet based Legendre spectrum
.sp
Author: Paulo Goncalves
.sp
Estimates the multifractal Legendre spectrum of a 1-D signal from the
wavelet coefficients of a \fBL1\fP continuous decomposition
.sp
.sp
.SH Usage
.sp
.ft CR
.nf
[alpha,f_alpha,logpart] = cwtspec(wt,scale,Q[,FindMax,ChooseReg])
.fi
.ec
.ft P
.sp
.SH Input parameters
.RS
.TP
o
\fBwt\fP : Real or complex matrix \f(CR[\fPN_scale,N\f(CR]\fP
Wavelet coefficients of a continuous wavelet transform (output of \fIcwt\fP)
.TP
o
\fBscale\fP : real vector \f(CR[\fP1,N_scale\f(CR]\fP
Analyzed scale vector
.TP
o
\fBQ\fP : real vector \f(CR[\fP1,N_Q\f(CR]\fP
Exponents of the partition function
.TP
o
\fBFindMax\fP : 0/1 flag.
\fIFindMax\fP = 0 : estimates the Legendre spectrum from all coefficients
\fIFindMax\fP = 1 : estimates the Legendre spectrum from the local Maxima
coefficients of the wavelet transform
Default value is FindMax = 1
.TP
o
\fBChooseReg\fP : 0/1 flag or integer vector \f(CR[\fP1,N_reg\f(CR]\fP,
(\fIN_reg\fP <= \fIN_scale\fP)
\fIChooseReg\fP = 0 : full scale range regression
\fIChooseReg\fP = 1 : asks online the scale indices setting the range for the linear
regression of the partition function.
\fIChooseReg\fP = \f(CR[\fPn1 ... nN_reg\f(CR]\fP : scale indices for the linear
regression of the partition function.
.RE
.SH Output parameters
.RS
.TP
o
\fBalpha\fP : Real vector \f(CR[\fP1,N_alpha\f(CR]\fP, \fIN_alpha\fP <= \fIN_Q\fP
Singularity support of the multifractal Legendre spectrum
.TP
o
\fBf_alpha\fP : real vector \f(CR[\fP1,N_alpha\f(CR]\fP
Multifractal Legendre spectrum
.TP
o
\fBlogpart\fP : real matrix \f(CR[\fPN_scale,N_Q\f(CR]\fP
Log-partition function
.TP
o
\fBtau\fP : real vector \f(CR[\fP1,N_Q\f(CR]\fP
Regression function
.RE
.SH See also:
cwt, contwtspec, contwt, dwtspec
.SH Example:
.sp
.ft CR
.nf
N = 2048 ; H = 0.7 ; Q = linspace(-4,4,11) ;
[x] = fbmlevinson(N,H) ;
[wt,scale] = cwt(x,2^(-8),2^(-1),16,8) ;
[alpha,f_alpha,logpart,tau] = cwtspec(wt,scale,Q,1,1) ;
plot(alpha,f_alpha),
.fi
.ec
.ft P
.sp
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