tr156.tex

语音处理平台 可以分析语音能量 第一振峰频率等数据

in table~\ref{tab:rice}.
\begin{table}[hbtp]
\begin{center} \begin{tabular}{|c|c|c|c|c|c|} \hline
	     	& sign	& lower	& number & full   \\
Number      	& bit	& bits	& of `0's & code   \\\hline
0		& 0	& 00	& 1	& 0001	 \\
13		& 0	& 01	& 3	& 0010001 \\
-7		& 1	& 11	& 2	& 111001 \\\hline
\end{tabular} \end{center}
\caption[nop]{Examples of Huffman codes for $n = 2$}
\label{tab:rice}
\end{table}

As with all Huffman codes, a whole number of bits are used per sample,
resulting in instantaneous decoding at the expense of introducing
quantization error in the p.d.f.  This is illustrated with the points
marked '$+$' in figure~\ref{fig:logpdf}.  In the example, $n = 2$ giving a
minimum code length of 4.  The error introduced by coding according to
the Laplacian p.d.f. instead of the true p.d.f. is only 0.004 bits per
sample, and the error introduced by using Huffman codes is only 0.12
bits per sample.  These are small compared to a typical code length of 7
for 16 kHz speech corpora.

This Huffman code is also simple in that it may be encoded and decoded
with a few logical operations.  Thus the implementation need not employ
a tree search for decoding, so reducing the computational and storage
overheads associated with transmitting a more general p.d.f.

The optimal number of low order bits to be transmitted directly is
linearly related to the variance of the signal.  The Laplacian is
defined as:
\begin{eqnarray}
p(x) & = & { 1 \over {\sqrt 2 } \sigma } e^{{- \sqrt 2 \over \sigma} | x |}
\end{eqnarray}
where $|x|$ is the absolute value of $x$ and $\sigma^2$ is the variance of the
distribution.  Taking the expectation of $|x|$ gives:
\begin{eqnarray}
E(|x|)	& = & \int_{-\infty}^\infty |x|  p(x) dx \\
	& = & \int_0^\infty x {{\sqrt 2} \over \sigma} e^{{- \sqrt 2 \over \sigma} x } dx \\
	& = & \int_0^\infty e^{{- \sqrt 2 \over \sigma} x } dx - 
	\left[ x e^{{- \sqrt 2 \over \sigma} x } \right]_0^\infty \\
	& = & {\sigma \over \sqrt 2}
\end{eqnarray}
For optimal Huffman coding we need to find the number of low order bits,
$n$, such that such that half the samples lie in the range $\pm 2^n$.
This ensures that the Huffman code is $n + 1$ bits long with probability
0.5 and $n + k + 1$ long with probability $2^{-(n + k)}$, which is
optimal.
\begin{eqnarray}
1/2 & = & \int_{-2^n}^{2^n} p(x) dx \\
    & = & \int_{-2^n}^{2^n}  { 1 \over {\sqrt 2 } \sigma } e^{{- \sqrt 2
\over \sigma} | x |} dx \\
    & = & - e^{{- \sqrt 2 \over \sigma} 2^n} + 1 \\
\end{eqnarray}
Solving for $n$ gives:
\begin{eqnarray}
n & = & \log_2 \left( \log(2) {\sigma \over \sqrt 2 } \right)\label{eq:n4lpc}\\
  & = & \log_2 \left(\log(2) E(|x|)  \right) \label{eq:n4poly}
\end{eqnarray}
When polynomial filters are used $n$ is obtained from $E(|x|)$ using
equation~\ref{eq:n4poly}.  In the LPC implementation $n$ is derived
from $\sigma$ which is obtained directly from the calculations for
predictor coefficients the using the autocorrelation method.

\section{Lossy coding}

The previous sections have outlined the complete waveform compression
algorithm for lossless coding.  There are a wide range of applications
whereby some loss in waveform accuracy is an acceptable tradeoff in
return for better compression.  A reasonably clean way to implement this
is to dynamically change the quantisation level on a segment-by-segment
basis.  Not only does this preserve the waveform shape, but the
resulting distortion can be easily understood.  Assuming that the
samples are uniformally distributed within the new quantisation interval
of $n$, then the probability of any one value in this range is $1/n$ and
the noise power introduced is $i^2$ for the lower values that are
rounded down and $(n -i)^2$ for those values that are rounded up.  Hence
the total noise power introduced by the increased quantisation is:
\begin{eqnarray}
{1 \over n } \left( \sum_{i=0}^{n / 2 - 1} i^2 + \sum_{i = n/2}^{n - 1}
(n -i)^2 \right) & = & {1 \over 12 } (n^2 + 2) \label{eq:quantnoise}
\end{eqnarray}
It may also be assumed that the signal was uniformally distributed in
the original quantisation interval before digitisation, i.e.\ a
quantisation error of $\int_{-1/2}^{1/2} x^2 {\rm d}x = 1/12$.

Shorten supports two main types of lossy coding: the case where every
segment is coded at the same rate; and the case where the bit rate is
dynamically adapted to maintain a specified segmental signal to noise
ratio.  In the first mode, the variance of the prediction residual of
the original waveform is estimated and then the appropriate quantisation
performed to limit the bit rate.  In areas of the waveform where there
are strong sample to sample correlations this results in a relatively
high signal to noise ratio, and in areas with little correlation the
signal to noise ratio approaches that of the signal power divided by the
quantisation noise of equation~\ref{eq:quantnoise}.  In the second mode,
this equation is used to estimate the greatest additional quantisation
that can be performed whilst maintaining a specified segmental signal to
noise ratio.  In both cases the new quantisation interval, $n$, is
restricted to be a power of two for computational efficiency.

\section{Compression Performance \label{ss:perf}}

The previous sections have demonstrated that low order linear prediction
followed by Huffman coding to the Laplace distribution results in an
efficient lossless waveform coder.  Table~\ref{tab:comp} compares this
technique to the popular general purpose compression utilities that are
available.  The table shows that the speech specific compression utility
can achieve considerably better compression than more general tools.
The compression and decompression speeds are the factors faster than
real time when executed on a standard SparcStation I, except the result
for the g722 ADPCM compression which was implemented on a SGI Indigo
R4400 workstation using the supplied aifccompress/aifcdecompress
utilities.  The SGI timings were scaled by a factor of 3.9 which was
determined by the relative execution times of shorten decompression on
the two platforms.
\begin{table}[htbp]
\begin{center}
\begin{tabular}{|l|r|r|r|}  \hline
program         	& \% size & compress	& decompress \\
			& 	  & speed 	& speed \\ \hline
UNIX compress   	& 74.0	  & 5.1 	& 15.0  \\
UNIX pack       	& 69.8	  & 16.1 	& 8.0   \\
GNU gzip        	& 66.0	  & 2.2 	& 17.2  \\
shorten default (fast)	& 42.6	  & 13.4	& 16.1  \\
shorten LPC (slow)	& 41.7 	  & 5.6		& 8.0	\\
aifc[de]compress	& lossy	  & 2.3		& 2.2	\\ \hline
\end{tabular}
\end{center}
\caption{Compression rates and speeds}
\label{tab:comp}
\end{table}

To investigate the effects of lossy coding on speech recognition
performance the test portion of the TIMIT database was coded at four
bits per sample and the resulting speech was recognised with a state of
the art phone recognition system.  Both shorten and the g722 ADPCM
standard gave negligible additional errors (about 70 more errors over
the baseline of 15934 errors), but it was necessary to apply a factor of
four scaling to the waveform for use with the g722 ADPCM algorithm.
g722 ADPCM without scaling and the telephony quality g721 ADPCM
algorithm (designed for 8kHz sampling and operated at 16kHz) both
produced significantly more errors (approximately 500 in 15934 errors).
Coding this database at four bit per sample results in approximately
another factor of two compression over lossless coding.

Decompression and playback of 16 bit, 44.1 kHz stereo audio takes
approximately 45\% of the available processing power of a 486DX2/66
based machine and 25\% of a 60 MHz Pentium.  Disk access accounted for
20\% of the time on the slower machine.  Performing compression to three
bits per sample gives another factor of three compression, reducing the
disk access time proportionally and providing 20\% faster execution with
no perceptual degradation (to the authors ears).  Thus real time
decompression of high quality audio is possible for a wide range of
personal computers.

\section{Conclusion}

This report has described a simple waveform coder designed for use with
stored waveform files.  The use of a simple linear predictor followed by
Huffman coding according to the Laplacian distribution has been found to
be appropriate for the examples studied.  Various techniques have been
adopted to improve the efficiency resulting in real time operation on
many platforms.  Lossy compression is supported, both to a specified bit
rate and to a specified signal to noise ratio.  Most simple sample file
formats are accepted resulting in a flexible tool for the workstation
environment.

\begin{thebibliography}{1}

\bibitem{GarofoloRobinsonFiscus94}
John Garofolo, Tony Robinson, and Jonathan Fiscus.
\newblock The development of file formats for very large speech corpora: Sphere
  and shorten.
\newblock In {\em Proc. ICASSP}, volume~I, pages 113--116, 1994.

\bibitem{JayantNoll84}
N.~S. Jayant and P.~Noll.
\newblock {\em Digital Coding of Waveforms}.
\newblock Prentice Hall, Englewood Cliffs, NJ, 1984.
\newblock ISBN 0-13-211913-7 01.

\bibitem{Rice71}
R.~F. Rice and J.~R. Plaunt.
\newblock Adaptive variable-length coding for efficient compression of
  spacecraft television data.
\newblock {\em IEEE Transactions on Communication Technology}, 19(6):889--897,
  1971.

\bibitem{YehRiceMiller91}
Pen-Shu Yeh, Robert Rice, and Warner Miller.
\newblock On the optimality of code options for a universal noisless coder.
\newblock JPL Publication 91-2, Jet Propulsion Laboratories, February 1991.

\bibitem{Rice91}
Robert~F. Rice.
\newblock Some practical noiseless coding techniques, {Part II, Module
  PSI14,K+}.
\newblock JPL Publication 91-3, Jet Propulsion Laboratories, November 1991.

\end{thebibliography}

\newpage
\section*{Appendix: The shorten man page (version 1.22)}

\begin{verbatim}
SHORTEN(1)               USER COMMANDS                 SHORTEN(1)


NAME
     shorten - fast compression for waveform files

SYNOPSIS
     shorten [-hl] [-a #bytes] [-b #samples] [-c  #channels]  [-d
     #bytes]  [-m  #blocks]  [-n  #dB] [-p #order] [-q #bits] [-r
     #bits]   [-t   filetype]   [-v   #version]    [waveform-file
     [shortened-file]]

     shorten -x [-hl] [ -a #bytes] [-d  #bytes]   [shortened-file
     [waveform-file]]

DESCRIPTION
     shorten reduces the size of waveform files (such  as  audio)
     using  Huffman  coding  of prediction residuals and optional
     additional quantisation.  In lossless  mode  the  amount  of
     compression  obtained depends on the nature of the waveform.
     Those composing of low frequencies and low  amplitudes  give
     the  best  compression,  which  may be 2:1 or better.  Lossy
     compression operates by specifying a minimum acceptable seg-
     mental  signal to noise ratio or a maximum bit rate.   Lossy
     compression operates by zeroing the lower order bits of  the
     waveform, so retaining waveform shape.

     If both file names are specified then these are used as  the
     input and output files.  The first file name can be replaced
     by "-" to read from standard input and likewise  the  second
     filename can be replaced by "-" to write to standard output.
     Under UNIX, if only one file name is  specified,  then  that
     name is used for input and the output file name is generated