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

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\hspace*{-1.6cm}\rule[0in]{16.5cm}{.02cm}
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{\bf \large \fontfamily{cmss}\selectfont Purpose}\\
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\begin{minipage}[t]{13.5cm}
Minimum mean cross-entropy combination of spectrograms.
\end{minipage}
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{\bf \large \fontfamily{cmss}\selectfont Synopsis}\\
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\begin{minipage}[t]{13.5cm}
\begin{verbatim}
[tfr,t,f] = tfrmmce(x)
[tfr,t,f] = tfrmmce(x,h)
[tfr,t,f] = tfrmmce(x,h,t)
[tfr,t,f] = tfrmmce(x,h,t,N)
[tfr,t,f] = tfrmmce(x,h,t,N,trace)
\end{verbatim}
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{\bf \large \fontfamily{cmss}\selectfont Description}\\
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        {\ty tfrmmce} computes the minimum mean cross-entropy combination
        of spectrograms using as windows the columns of the matrix {\ty
        h}. The expression of this distribution writes 

\[\Pi_x(t,\nu)=\dfrac{E}{\| \Pi_{k=1}^N |F_x(t,\nu;h_k)|^{2/N}\|_1}\
{\displaystyle \Pi_{k=1}^N} |F_x(t,\nu;h_k)|^{2/N}, \]

where $\|\ \|_1$ denotes the $L_1$ norm, $E$ the energy of the signal\,:
\[E=\int_{-\infty}^{+\infty} |x(t)|^2\ dt=\iint_{-\infty}^{+\infty}
\Pi_x(t,\nu)\ dt\ d\nu=\|\Pi_x(t,\nu)\|_1,\] and $F_x(t,\nu;h_k)$ the
short-time Fourier transform of $x$, with analysis window $h_k(t)$.\\

\hspace*{-.5cm}\begin{tabular*}{14cm}{p{1.5cm} p{8cm} c}
Name & Description & Default value\\
\hline
        {\ty x}     & signal ({\ty Nx=length(x)})\\
        {\ty h}     & frequency smoothing windows, the {\ty h(:,i)} being normalized
                so as to be of unit energy\\
        {\ty t}     & time instant(s)          & {\ty (1:Nx)}\\
        {\ty  N}    & number of frequency bins & {\ty Nx}\\
        {\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 tfrmmce} runs {\ty tfrqview}.
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\newpage

{\bf \large \fontfamily{cmss}\selectfont Example}\\
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Here is a combination of three spectrograms with gaussian analysis windows
of different lengths :
\begin{verbatim}
         sig=fmlin(128,0.1,0.4); h=zeros(19,3);
         h(10+(-5:5),1)=window(11); 
         h(10+(-7:7),2)=window(15);  
         h(10+(-9:9),3)=window(19); 
         tfrmmce(sig,h);
\end{verbatim}
\end{minipage}
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{\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] P. Loughlin, J. Pitton, B. Hannaford ``Approximating Time-Frequency
Density Functions via Optimal Combinations of Spectrograms'' IEEE Signal
Processing Letters, Vol. 1, No. 12, Dec. 1994. 
\end{minipage}