[SPTK-CVS] SPTK/doc/ref_e rlevdur.tex, NONE, 1.1 Makefile.in, 1.37, 1.38 main.tex, 1.59, 1.60 levdu

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Update of /cvsroot/sp-tk/SPTK/doc/ref_e
In directory sfp-cvs-1.v30.ch3.sourceforge.com:/tmp/cvs-serv15760

Modified Files:
	Makefile.in main.tex levdur.tex 
Added Files:
	rlevdur.tex 
Log Message:
add manual of rlevdur command and modify manual of levdur command

Index: Makefile.in
===================================================================
RCS file: /cvsroot/sp-tk/SPTK/doc/ref_e/Makefile.in,v
retrieving revision 1.37
retrieving revision 1.38
diff -C2 -d -r1.37 -r1.38
*** Makefile.in	31 Jul 2017 06:09:47 -0000	1.37
--- Makefile.in	29 Sep 2017 10:16:57 -0000	1.38
***************
*** 151,154 ****
--- 151,155 ----
  	ramp.tex \
  	reverse.tex \
+ 	rlevdur.tex \
  	rmse.tex \
  	root_pol.tex \

Index: levdur.tex
===================================================================
RCS file: /cvsroot/sp-tk/SPTK/doc/ref_e/levdur.tex,v
retrieving revision 1.25
retrieving revision 1.26
diff -C2 -d -r1.25 -r1.26
*** levdur.tex	16 May 2017 10:58:48 -0000	1.25
--- levdur.tex	29 Sep 2017 10:16:57 -0000	1.26
***************
*** 43,57 ****
  % ----------------------------------------------------------------- %
  \hypertarget{levdur}{}
! \name{levdur}{solve an autocorrelation normal equation 
                      using Levinson-Durbin method}{signal processing}

  \begin{synopsis}
!  \item [levdur] [ --m $M$ ] [ --f $F$ ] [ {\em infile} ] 
  \end{synopsis}

  \begin{qsection}{DESCRIPTION}
! {\em levdur} calculates linear prediction coefficients (LPC) 
! from the autocorrelation matrix from {\em infile} (or standard input), 
  sending the result to standard output.

--- 43,57 ----
  % ----------------------------------------------------------------- %
  \hypertarget{levdur}{}
! \name{levdur}{solve an autocorrelation normal equation
                      using Levinson-Durbin method}{signal processing}

  \begin{synopsis}
!  \item [levdur] [ --m $M$ ] [ --f $F$ ] [ {\em infile} ]
  \end{synopsis}

  \begin{qsection}{DESCRIPTION}
! {\em levdur} calculates linear prediction coefficients (LPC)
! from the autocorrelation matrix from {\em infile} (or standard input),
  sending the result to standard output.

***************
*** 60,64 ****
    r(0),r(1),\dots,r(M).
  \end{displaymath}
! {\em levdur} uses the Levinson-Durbin algorithm 
  to solve a system of linear equations
  obtained from the autocorrelation matrix.
--- 60,64 ----
    r(0),r(1),\dots,r(M).
  \end{displaymath}
! {\em levdur} uses the Levinson-Durbin algorithm
  to solve a system of linear equations
  obtained from the autocorrelation matrix.
***************
*** 69,73 ****
  $K, a(1), \dots, a(M)$ of an all-pole digital filter
  \begin{displaymath}
! H(z) = \frac{K}{\displaystyle{1+\sum_{i=1}^{M}a(k)z^{-i}}}.
  \end{displaymath}
  The linear prediction coefficients are evaluated by solving
--- 69,73 ----
  $K, a(1), \dots, a(M)$ of an all-pole digital filter
  \begin{displaymath}
! H(z) = \frac{K}{\displaystyle{1+\sum_{i=1}^{M}a(i)z^{-i}}}.
  \end{displaymath}
  The linear prediction coefficients are evaluated by solving
***************
*** 87,91 ****
  	a(M) \\
  \end{pmatrix}
! = - 
  \begin{pmatrix}
  	r(1) \\
--- 87,91 ----
  	a(M) \\
  \end{pmatrix}
! = -
  \begin{pmatrix}
  	r(1) \\
***************
*** 103,107 ****
  		{E^{(i-1)}} \label{eqn:lev_dur_k}\notag\\
  a^{(i)}(i) &= k(i) \notag\\
! a^{(i)}(j) &=  a^{(i-1)}(j) + k(i) a^{(i-1)}(i-j), 
  		\qquad 1\leq j \leq i-1\\
  E^{(i)}    &= (1-k^2(i)) E^{(i-1)} \label{eqn:lev_dur_E}
--- 103,107 ----
  		{E^{(i-1)}} \label{eqn:lev_dur_k}\notag\\
  a^{(i)}(i) &= k(i) \notag\\
! a^{(i)}(j) &=  a^{(i-1)}(j) + k(i) a^{(i-1)}(i-j),
  		\qquad 1\leq j \leq i-1\\
  E^{(i)}    &= (1-k^2(i)) E^{(i-1)} \label{eqn:lev_dur_E}
***************
*** 126,134 ****
  \begin{quote}
   \verb!frame < data.f | window | acorr -m 25 | levdur > data.lpc!
! \end{quote} 
  \end{qsection}

  \begin{qsection}{NOTICE}
! The default value for -f option is zero as a trial. In the previous version, the 
  default value is 1.0E-6.
  \end{qsection}
--- 126,134 ----
  \begin{quote}
   \verb!frame < data.f | window | acorr -m 25 | levdur > data.lpc!
! \end{quote}
  \end{qsection}

  \begin{qsection}{NOTICE}
! The default value for -f option is zero as a trial. In the previous version, the
  default value is 1.0E-6.
  \end{qsection}
***************
*** 136,139 ****
  \begin{qsection}{SEE ALSO}
  \hyperlink{acorr}{acorr},
! \hyperlink{lpc}{lpc}
  \end{qsection}
--- 136,140 ----
  \begin{qsection}{SEE ALSO}
  \hyperlink{acorr}{acorr},
! \hyperlink{lpc}{lpc},
! \hyperlink{rlevdur}{rlevdur}
  \end{qsection}

--- NEW FILE: rlevdur.tex ---
% ----------------------------------------------------------------- %
%             The Speech Signal Processing Toolkit (SPTK)           %
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% ----------------------------------------------------------------- %
\hypertarget{rlevdur}{}
\name{rlevdur}{solve an autocorrelation normal equation using reverse Levinson-Durbin method}{signal processing}

\begin{synopsis}
\item [rlevdur] [ --m $M$ ] [ {\em infile} ]
\end{synopsis}

\begin{qsection}{DESCRIPTION}
{\em rlevdur} calculates the autocorrelation matrix from the linear
prediction coefficients (LPC) from {\em infile} (or standard input),
sending the result to standard output.

The input is the $M$-th order linear prediction coefficients which are
the set of coefficients $K, a(1), \dots, a(M)$ of an all-pole digital filter
\begin{displaymath}
H(z) = \frac{K}{\displaystyle{1+\sum_{i=1}^{M}a(i)z^{-i}}}.
\end{displaymath}

{\em rlevdur} uses the reverse Levinson-Durbin algorithm
to solve a system of linear equations
obtained from linear prediction coefficients.

Input and output data are in float format.

The output is the $M$-th order autocorrelation matrix
\begin{displaymath}
  r(0),r(1),\dots,r(M).
\end{displaymath}
The autocorrelation matrix are evaluated by solving
the following set of linear equations, which were obtained
through the autocorrelation method,
\begin{displaymath}
\begin{pmatrix}
        r(0) & r(1) & \dots & r(M-1) \\
        r(1) & r(0) &        & \vdots \\
        \vdots &    & \ddots &         \\
        r(M-1) &    & \dots & r(0)   \\
\end{pmatrix}
\begin{pmatrix}
	a(1) \\
	a(2) \\
	\vdots \\
	a(M) \\
\end{pmatrix}
= -
\begin{pmatrix}
	r(1) \\
	r(2) \\
	\vdots \\
	r(M) \\
\end{pmatrix}
\end{displaymath}
The Durbin iterative and efficient algorithm is used
to solve the system above. It takes advantage of the Toeplitz characteristic
of the autocorrelation matrix.
\end{qsection}

\begin{options}
	\argm{m}{M}{order of correlation}{25}
\end{options}

\begin{qsection}{EXAMPLE}
In this example, the linear prediction coefficients in float format
are read from {\em data.lpc} and the CSM coefficients are written to
{\em data.csm}:
\begin{quote}
 \verb!lpc < data.lpc | rlevdur | acr2csm > data.csm!
\end{quote}
\end{qsection}

\begin{qsection}{SEE ALSO}
\hyperlink{lpc}{lpc},
\hyperlink{acr2csm}{acr2csm},
\hyperlink{levdur}{levdur}
\end{qsection}

Index: main.tex
===================================================================
RCS file: /cvsroot/sp-tk/SPTK/doc/ref_e/main.tex,v
retrieving revision 1.59
retrieving revision 1.60
diff -C2 -d -r1.59 -r1.60
*** main.tex	31 Jul 2017 06:09:47 -0000	1.59
--- main.tex	29 Sep 2017 10:16:57 -0000	1.60
***************
*** 274,277 ****
--- 274,278 ----
  \include{raw2wav}
  \include{reverse}
+ \include{rlevdur}
  \include{rmse}
  \include{root_pol}

[SPTK-CVS] SPTK/doc/ref_e rlevdur.tex, NONE, 1.1 Makefile.in, 1.37, 1.38 main.tex, 1.59, 1.60 levdu

[SPTK-CVS] SPTK/doc/ref_e rlevdur.tex, NONE, 1.1 Makefile.in, 1.37, 1.38 main.tex, 1.59, 1.60 levdur.tex, 1.25, 1.26