# [xiph-cvs] cvs commit: speex/doc manual.lyx

Jean-Marc Valin jm at xiph.org
Tue Nov 26 18:54:35 PST 2002


jm          02/11/26 21:54:34

Modified:    doc      manual.lyx
Log:
...

Revision  Changes    Path
1.36      +49 -16    speex/doc/manual.lyx

Index: manual.lyx
===================================================================
RCS file: /usr/local/cvsroot/speex/doc/manual.lyx,v
retrieving revision 1.35
retrieving revision 1.36
diff -u -r1.35 -r1.36
--- manual.lyx	13 Nov 2002 04:03:04 -0000	1.35
+++ manual.lyx	27 Nov 2002 02:54:34 -0000	1.36
@@ -494,17 +494,18 @@

\layout Standard

-During voiced segments, the speech signal is very periodic, so it is possible
- to take advantage of that by expressing the excitation signal
-\begin_inset Formula $e(n)$
+During voiced segments, the speech signal is periodic, so it is possible
+ to take advantage of that property by approximating the excitation signal
+
+\begin_inset Formula $e[n]$
\end_inset

- as
+ by a gain times the past of the excitation:
\layout Standard

\begin_inset Formula $-e[n]=\beta e[n-T]+c[n]$
+e[n]\simeq p[n]=\beta e[n-T]\]

\end_inset

@@ -528,28 +529,60 @@
innovation codebook
\emph default
.
- In the
+ We call that long-term prediction since the excitation is predicted from
+
+\begin_inset Formula $e[n-T]$
+\end_inset
+
+ with
+\begin_inset Formula $T\gg N$
+\end_inset
+
+.
+\layout Subsection
+
+Innovation Codebook
+\layout Standard
+
+The final excitation
+\begin_inset Formula $e[n]$
+\end_inset
+
+ will be the sum of the pitch prediction and an
\emph on
-z
+innovation
\emph default
--domain, the excitation can be expressed as:
+ signal
+\begin_inset Formula $c[n]$
+\end_inset
+
+ taken from a fixed codebook.
\layout Standard

\begin_inset Formula $-e(z)=\frac{1}{1-\beta z^{-T}}\: c(z)$
+e[n]=p[n]+c[n]=\beta e[n-T]+c[n]\]

\end_inset

-
-\layout Subsection
-
-Innovation Codebook
-\layout Standard
-
This is where most of the bits in a CELP codec are allocated.
It represents the information that couldn't be obtained either from linear
prediction or pitch prediction.
+ In the
+\emph on
+z
+\emph default
+-domain we can represent the final signal
+\begin_inset Formula $X(z)$
+\end_inset
+
+ as
+\begin_inset Formula $+X(z)=\frac{C(z)}{A(z)\left(1-\beta z^{-T}\right)}$
+
+\end_inset
+
+
\layout Subsection

Analysis-by-Synthesis and Error Weighting
@@ -2286,7 +2319,7 @@

\layout Standard

-(Tones/DTMF to be implemented)
+reserved
\end_inset
</cell>
</row>

<p><p>--- >8 ----
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