tfrcw.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.


\markright{tfrcw}
\hspace*{-1.6cm}{\Large \bf tfrcw}

\vspace*{-.4cm}
\hspace*{-1.6cm}\rule[0in]{16.5cm}{.02cm}
\vspace*{.2cm}

{\bf \large \fontfamily{cmss}\selectfont Purpose}\\
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\begin{minipage}[t]{13.5cm}
Choi-Williams time-frequency distribution.
\end{minipage}
\vspace*{.5cm}

{\bf \large \fontfamily{cmss}\selectfont Synopsis}\\
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\begin{minipage}[t]{13.5cm}
\begin{verbatim}
[tfr,t,f] = tfrcw(x)
[tfr,t,f] = tfrcw(x,t)
[tfr,t,f] = tfrcw(x,t,N)
[tfr,t,f] = tfrcw(x,t,N,g)
[tfr,t,f] = tfrcw(x,t,N,g,h)
[tfr,t,f] = tfrcw(x,t,N,g,h,sigma)
[tfr,t,f] = tfrcw(x,t,N,g,h,sigma,trace)
\end{verbatim}
\end{minipage}
\vspace*{.5cm}

{\bf \large \fontfamily{cmss}\selectfont Description}\\
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\begin{minipage}[t]{13.5cm}
        {\ty tfrcw} computes the Choi-Williams distribution of a
        discrete-time signal {\ty x}, or the cross Choi-Williams
        representation between two signals. This distribution has the
        following expression :

\[CW_x(t,\nu)=2
\iint_{-\infty}^{+\infty} \dfrac{\sqrt{\sigma}}{4\sqrt{\pi}|\tau|}\
e^{-v^2\sigma/(16\tau^2)}\ x(t+v+\frac{\tau}{2})\
x^*(t+v-\frac{\tau}{2})\ e^{-j2\pi \nu \tau}\ dv\ d\tau.\]

\hspace*{-.5cm}\begin{tabular*}{14cm}{p{1.5cm} p{8cm} c}
Name & Description & Default value\\
\hline
        {\ty x}     & signal if auto-CW, or {\ty [x1,x2]} if cross-CW {\ty
			(Nx=length(x))}\\
        {\ty t}     & time instant(s)          & {\ty (1:Nx)}\\
        {\ty N}     & number of frequency bins & {\ty Nx}\\
        {\ty g}     & time smoothing window, {\ty G(0)} being forced to {\ty 1}, where {\ty G(f)} is the Fourier transform of {\ty g(t)}
              &                           {\ty window(odd(N/10))}\\
        {\ty h}     & frequency smoothing window, {\ty h(0)} being forced to {\ty 1}
              &                           {\ty window(odd(N/4))}\\ 
        {\ty sigma} & kernel width             & {\ty 1}\\
        {\ty trace} & if nonzero, the progression of the algorithm is shown
              &                           {\ty 0}\\
     \hline {\ty tfr}   & time-frequency representation\\
        {\ty f}     & vector of normalized frequencies\\

\hline
\end{tabular*}
\vspace*{.2cm}

When called without output arguments, {\ty tfrcw} runs {\ty tfrqview}.
\end{minipage}

\newpage

{\bf \large \fontfamily{cmss}\selectfont Example}
\begin{verbatim}
         sig=fmlin(128,0.05,0.3)+fmlin(128,0.15,0.4);  
         g=window(9,'Kaiser'); h=window(27,'Kaiser'); 
         t=1:128; tfrcw(sig,t,128,g,h,3.6,1);
\end{verbatim}
\vspace*{.5cm}

{\bf \large \fontfamily{cmss}\selectfont See Also}\\
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\begin{minipage}[t]{13.5cm}
all the {\ty tfr*} functions.
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{\bf \large \fontfamily{cmss}\selectfont Reference}\\
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\begin{minipage}[t]{13.5cm}
[1] H. Choi, W. Williams ``Improved Time-Frequency Representation of
Multicomponent Signals Using Exponential Kernels'', IEEE Trans. on
Acoustics, Speech and Signal Processing, Vol. 37, No. 6, June 1989.
\end{minipage}