% 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{gdpower}
\section*{\hspace*{-1.6cm} gdpower}

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



{\bf \large \sf Purpose}\\
\hspace*{1.5cm}
\begin{minipage}[t]{13.5cm}
Signal with a power-law group delay.
\end{minipage}
\vspace*{.5cm}


{\bf \large \sf Synopsis}\\
\hspace*{1.5cm}
\begin{minipage}[t]{13.5cm}
\begin{verbatim}
[x,gpd,f] = gdpower(N)
[x,gpd,f] = gdpower(N,k)
[x,gpd,f] = gdpower(N,k,c)
\end{verbatim}
\end{minipage}
\vspace*{.5cm}


{\bf \large \sf Description}\\
\hspace*{1.5cm}
\begin{minipage}[t]{13.5cm}
        {\ty gdpower} generates a signal with a power-law group delay of
        the form \[t_x(f) = t_0 + c\ f^{k-1}.\] The output signal is of
        unit energy.\\
 
\hspace*{-.5cm}\begin{tabular*}{14cm}{p{1.5cm} p{8.5cm} c}
Name & Description & Default value\\
\hline
        {\ty N}   & number of points in time          (must be even)\\
        {\ty k}   & degree of the power-law           & {\ty 0}\\
        {\ty c}   & rate-coefficient of the power-law group delay.  
              {\ty c} must be non-zero.               & {\ty 1} \\  
  \hline {\ty x}   & time row vector containing the signal samples\\
        {\ty gpd} & output vector containing the group delay samples, of
	length {\ty round(N/2)}\\ 
        {\ty f}   & frequency bins\\
\hline
\end{tabular*}

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


{\bf \large \sf Examples}\\
\hspace*{1.5cm}
\begin{minipage}[t]{13.5cm}
Consider a hyperbolic group-delay law, and compute the Bertrand
distribution of it :
\begin{verbatim}
         sig=gdpower(128); 
         tfrbert(sig,1:128,0.01,0.3,128,1);
\end{verbatim}
We note that the perfect localization property of the Bertrand distribution
on hyperbolic group-delay signals is checked in that case. \\
\end{minipage}
\newpage
\hspace*{1.5cm}\begin{minipage}[t]{13.5cm}
Plot the instantaneous frequency law on which the D-Flandrin distribution
is perfectly concentrated :
\begin{verbatim}
         [sig,gpd,f]=gdpower(128,1/2); 
         plot(gpd,f); 
         tfrdfla(sig,1:128,.01,.3,218,1);
\end{verbatim}
\end{minipage}
\vspace*{.5cm}


{\bf \large \sf See Also}\\
\hspace*{1.5cm}
\begin{minipage}[t]{13.5cm}
\begin{verbatim}
fmpower.
\end{verbatim}
\end{minipage}

