loctime.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{loctime}
\hspace*{-1.6cm}{\Large \bf loctime}

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



{\bf \large \fontfamily{cmss}\selectfont Purpose}\\
\hspace*{1.5cm}
\begin{minipage}[t]{13.5cm}
Time localization characteristics.
\end{minipage}
\vspace*{.5cm}


{\bf \large \fontfamily{cmss}\selectfont Synopsis}\\
\hspace*{1.5cm}
\begin{minipage}[t]{13.5cm}
\begin{verbatim}
[tm,T] = loctime(x)
\end{verbatim}
\end{minipage}
\vspace*{.5cm}


{\bf \large \fontfamily{cmss}\selectfont Description}\\
\hspace*{1.5cm}
\begin{minipage}[t]{13.5cm}
        {\ty loctime} computes the time localization characteristics of
        signal {\ty x}. The definition used for the averaged time
        and the time spreading are the following\,:
\begin{eqnarray*}
t_m &=& \frac{1}{E_x}\ \int_{-\infty}^{+\infty} t\ |x(t)|^2\ dt \\ T &=&
2\ \sqrt{\frac{\pi}{E_x}\ \int_{-\infty}^{+\infty} (t-t_m)^2\ |x(t)|^2\ dt}
\end{eqnarray*}
where $E_x$ is the energy of the signal. With this definition (and the one
used in {\ty locfreq}), the Heisenberg-Gabor inequality writes $B\ T\geq
1$.\\

\hspace*{-.5cm}\begin{tabular*}{14cm}{p{1.5cm} p{8.5cm} c}
Name & Description & Default value\\
\hline
   {\ty x}   & signal\\
 \hline       {\ty tm}  & averaged time center\\
        {\ty T}   & time spreading\\

\hline
\end{tabular*}

\end{minipage}
\vspace*{1cm}

{\bf \large \fontfamily{cmss}\selectfont Examples}\\
\hspace*{1.5cm}
\begin{minipage}[t]{13.5cm}
Here is an example of signal which corresponds to the lower bound of the
Heisenberg-Gabor inequality.
\begin{verbatim}
         z=amgauss(160,80,50); 
         [tm,T]=loctime(z); 
         [fm,B]=locfreq(z);
         [tm,T,fm,B,T*B]
         ans = 
               80.0000   50.0000   0.0000   0.0200   1
\end{verbatim}
\end{minipage}
\vspace*{.5cm}


{\bf \large \fontfamily{cmss}\selectfont See Also}\\
\hspace*{1.5cm}
\begin{minipage}[t]{13.5cm}
\begin{verbatim}
locfreq.
\end{verbatim}
\end{minipage}