scale.tex

时频分析的工具包

% This is part of the TFTB Reference Manual.
% Copyright (C) 1996 CNRS (France) and Rice University (US).
% See the file refguide.tex for copying conditions.


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\hspace*{-1.6cm}{\Large \bf scale}

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{\bf \large \fontfamily{cmss}\selectfont Purpose}\\
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\begin{minipage}[t]{13.5cm}
Scale a signal using the Mellin transform.
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{\bf \large \fontfamily{cmss}\selectfont Synopsis}\\
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\begin{verbatim}
S = scale(x,a,fmin,fmax,N)
\end{verbatim}
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{\bf \large \fontfamily{cmss}\selectfont Description}\\
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        {\ty scale} computes the {\ty a}-scaled version of signal {\ty x} :
        $x_a(t)\ =\ a^{-\frac{1}{2}}\ x(\frac{t}{a})$ using the Mellin
        transform.\\
 
\hspace*{-.5cm}\begin{tabular*}{14cm}{p{1.5cm} p{8.5cm} c}
Name & Description & Default value\\
\hline
        {\ty x} & signal in time to be scaled ({\ty Nx=length(x)})\\
        {\ty a} & scale factor. {\ty a} $<$ 1 corresponds to a compression
		in the time domain and {\ty a} $>$ 1 to a dilation. {\ty a}
		can be a vector. 		& {\ty 2}\\ 
        {\ty fmin, fmax} & respectively lower and upper frequency bounds of 
           the analyzed signal. These parameters fix the equivalent 
           frequency bandwidth (expressed in Hz). When unspecified, you
           have to enter them at the command line from the plot of the
           spectrum. {\ty fmin} and {\ty fmax} must be $>${\ty 0} and
	   $\leq${\ty 0.5}\\ 
        {\ty N} & number of analyzed voices & auto\footnote{This value,
	determined from {\ty fmin} and {\ty fmax}, is the 
	next-power-of-two of the minimum value checking the non-overlapping
	condition in the fast Mellin transform.}\\
\hline  {\ty S} & the {\ty a}-scaled version of signal {\ty x}. Length of
		{\ty S} can be larger than length of {\ty x} if {\ty a} $>$
		1. If {\ty a} is a vector of length {\ty L}, {\ty S} is  
           a matrix with {\ty L} columns. {\ty S} has the same energy as {\ty x}.\\
\hline
\end{tabular*}
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{\bf \large \fontfamily{cmss}\selectfont Example}\\
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Dilate a Klauder-wavelet by a factor of 2 :
\begin{verbatim}
         sig=klauder(100); S=scale(sig,2,.05,.45,100);
         subplot(211); plot(sig); 
         subplot(212); plot(real(S(51:150)));
\end{verbatim}
\end{minipage}
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{\bf \large \fontfamily{cmss}\selectfont See Also}\\
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fmt.
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