speechio.tex

隐马尔科夫模型工具箱

Independent of what parameter kind is required, there are some simple
pre-processing operations that can be applied prior to performing the actual
signal analysis.\index{speech input!pre-processing} 
Firstly, the DC mean can be removed from the source waveform by setting the
Boolean configuration parameter
\texttt{ZMEANSOURCE}\index{zmeansource@\texttt{ZMEANSOURCE}} to true 
(i.e.\ \texttt{T}). This is useful when\index{speech input!DC offset}
the original analogue-digital conversion has added a DC offset to the
signal. It is applied to each window individually so that it can be
used both when reading from a file and when using direct audio
input\footnote{ This method of applying a zero mean is different to
HTK Version 1.5 where the mean was calculated and subtracted from the
whole speech file in one operation. The configuration variable
\texttt{V1COMPAT} can be set to revert to this older behaviour.}.

Secondly,  it is common practice to pre-emphasise
the signal by applying the first order difference equation
\hequation{
   {s^{\prime}}_n  = s_n - k\,s_{n-1}
}{preemp}
to the samples\index{speech input!pre-emphasis}
$\{s_n, n=1,N \}$ in each window.  Here $k$ is the
pre-emphasis\index{pre-emphasis} coefficient which should be in the range
$0 \leq k < 1$.  It is specified using the configuration
parameter \texttt{PREEMCOEF}\index{preemcoef@\texttt{PREEMCOEF}}.
Finally,
it is usually beneficial to taper the
samples in each window so that discontinuities at the window
edges are attenuated.  This is done by setting the
Boolean configuration 
parameter \texttt{USEHAMMING}\index{usehamming@\texttt{USEHAMMING}}
to true.
This applies the following transformation to the samples
$\{s_n, n=1,N\}$ in the window
\hequation{
   {s^{\prime}}_n = \left\{ 0.54 - 0.46 \cos \left( \frac{2 \pi (n-1)}{N-1}
         \right) \right\} s_n
}{ham}
When both pre-emphasis and Hamming windowing are enabled,
pre-emphasis is performed 
first.\index{speech input!Hamming window function} \index{Hamming Window}

In practice, all three of the above are usually applied.
Hence, a configuration file will typically contain the 
following
\begin{verbatim}
    ZMEANSOURCE = T
    USEHAMMING = T
    PREEMCOEF = 0.97
\end{verbatim}
Certain types of artificially generated waveform data can cause numerical
overflows with some coding schemes. In such cases adding a small amount of
random noise to the waveform data solves the problem. The noise is added
to the samples using
\hequation{
   {s^{\prime}}_n = s_n + q RND()
}{dither}
where $RND()$ is a uniformly distributed random value over the interval
$[-1.0, +1.0)$ and $q$ is the scaling factor. The amount of noise added 
to the data ($q$) is set with the configuration parameter
\index{adddither@\texttt{ADDDITHER}}\texttt{ADDDITHER} (default value $0.0$). 
A positive value causes the noise signal added to be the same every time
(ensuring that the same file always gives exactly the same results). With a
negative value the noise is random and the same file may produce slightly
different results in different trials.

One problem that can arise when processing speech waveform files obtained from
external sources, such as databases on CD-ROM, is that the
byte-order\index{byte-order} may be different to that used by the machine on
which \HTK\ is running. To deal with this problem, \htool{HWave} can perform
automatic byte-swapping in order to preserve proper byte order. \HTK\ assumes
by default that speech waveform data is encoded as a sequence of 2-byte
integers as is the case for most current speech databases\footnote{Many of the
more recent speech databases use compression. In these cases, the data may be
regarded as being logically encoded as a sequence of 2-byte integers even if
the actual storage uses a variable length encoding scheme.}. 
If the source format is known, then \htool{HWave} will also make an assumption
about the byte order used to create speech files in that format. It then checks
the byte order of the machine that it is running on and automatically performs
byte-swapping if the order is different. For unknown formats, proper byte order
can be ensured by setting the configuration parameter
\texttt{BYTEORDER}\index{byteorder@\texttt{BYTEORDER}} to \texttt{VAX} if the
speech data was created on a little-endian machine such as a VAX or an IBM PC,
and to anything else (e.g. \texttt{NONVAX}) if the speech data was created on a
big-endian machine such as a SUN, HP or Macintosh machine. \index{speech
input!byte order} 

The reading/writing of \HTK\ format waveform files can be further controlled
via the configuration parameters \texttt{NATURALREADORDER} and 
\texttt{NATURALWRITEORDER}. The effect and default settings of these parameters
are described in section~\href{s:byteswap}.
\index{byte swapping}
Note that \texttt{BYTEORDER} should not be used when \texttt{NATURALREADORDER}
is set to true.  Finally, note that \HTK\ can also byte-swap parameterised
files in a similar way provided that only the byte-order of each 4 byte float
requires inversion.  

\mysect{Linear Prediction Analysis}{lpcanal}

In linear prediction (LP) \index{linear prediction} analysis, the 
vocal tract transfer function
is modelled by an all-pole filter\index{all-pole filter} with transfer function\footnote{
Note that some textbooks define the denominator of equation~\ref{e:allpole}
as $1 - \sum_{i=1}^p a_i z^{-i}$ so that the filter coefficients are the
negatives of those computed by \HTK.}
\hequation{
H(z) = \frac{1}{\sum_{i=0}^p a_i z^{-i}}
}{allpole}
where $p$ is the number of poles and $a_0 \equiv 1$.
The filter coefficients $\{a_i \}$ are chosen to minimise
the mean square filter prediction error summed over the analysis
window.  The \HTK\ module \htool{HSigP} uses the \textit{autocorrelation
method} to perform this optimisation as follows.

Given a window of speech samples $\{s_n, n=1,N \}$,
the first $p+1$ terms of the autocorrelation sequence are
calculated from
\hequation{
r_i = \sum_{j=1}^{N-i} s_j s_{j+i}
}{autoco}
where $i = 0,p$.
The filter coefficients are then computed recursively
using a set of auxiliary coefficients $\{k_i\}$ which can be
interpreted as the reflection coefficients of an equivalent
acoustic tube and the prediction error $E$ which is initially
equal to $r_0$.  Let $\{k_j^{(i-1)} \}$ and $\{a_j^{(i-1)} \}$
be the reflection and filter coefficients for a filter of order
$i-1$, then a filter of order $i$ can be calculated in three steps.
Firstly, a new set of reflection coefficients\index{reflection coefficients} are calculated.
\hequation{
 k_j^{(i)} = k_j^{(i-1)}
}{kupdate1}
for $j = 1,i-1$ and
\hequation{
 k_i^{(i)} =  \left\{ r_i + 
          \sum_{j=1}^{i-1} a_j^{(i-1)} r_{i-j} \right\} / E^{(i-1)}
}{kupdate2}
Secondly, the prediction energy is updated.
\hequation{
E^{(i)} = (1 -  k_i^{(i)}  k_i^{(i)} ) E^{(i-1)}
}{Eupdate}
Finally, new filter coefficients are computed
\hequation{
a_j^{(i)} = a_j^{(i-1)} - k_i^{(i)} a_{i-j}^{(i-1)}
}{aupdate1}
for $j = 1,i-1$ and
\hequation{
a_i^{(i)} = - k_i^{(i)} 
}{aupdate2}
This process is repeated from $i=1$ through to the required filter order
$i=p$.

To effect the above transformation, the target parameter kind must
be set to either \texttt{LPC}\index{lpc@\texttt{LPC}} to obtain the LP filter parameters $\{a_i\}$ or
\texttt{LPREFC}\index{lprefc@\texttt{LPREFC}} to obtain the reflection coefficients  $\{k_i \}$.  The
required filter order must also be set using the configuration
parameter \texttt{LPCORDER}\index{lpcorder@\texttt{LPCORDER}}.
Thus, for example, the following configuration
settings would produce a target parameterisation
consisting of 12 reflection coefficients per vector.
\begin{verbatim}
    TARGETKIND = LPREFC
    LPCORDER = 12
\end{verbatim}

An alternative LPC-based parameterisation is obtained by setting the
target kind to  \texttt{LPCEPSTRA}\index{lpcepstra@\texttt{LPCEPSTRA}} to generate linear prediction cepstra.  
The cepstrum of a signal is computed by taking a Fourier (or similar)
transform of the log spectrum.  In the case of linear 
prediction cepstra\index{linear prediction!cepstra}, the
required spectrum is the linear prediction spectrum which can be obtained
from the Fourier transform of the filter coefficients. However, it can be shown
that the required cepstra can be more efficiently computed using 
a simple recursion
\hequation{
   c_n = -a_n - \frac{1}{n} \sum_{i=1}^{n-1} (n-i) a_i c_{n-i}
}{lpcepstra}
The number of cepstra generated need not be the same as the number of
filter coefficients, hence it is set by a separate configuration 
parameter called \texttt{NUMCEPS}\index{numceps@\texttt{NUMCEPS}}.

The principal advantage of cepstral coefficients is that they are 
generally decorrelated and this allows diagonal covariances
to be used in the HMMs.  However, one minor problem with 
them is that the higher order cepstra are numerically quite small and 
this results in
a very wide range of variances when going from the low to high cepstral 
coefficients\index{cepstral coefficients!liftering}.
\HTK\ does not have a problem with this but for pragmatic reasons such as
displaying model parameters, flooring variances, etc., it is convenient to re-scale
the cepstral coefficients to have similar magnitudes.  This is done by
setting the configuration parameter \texttt{CEPLIFTER}\index{ceplifter@\texttt{CEPLIFTER}} to some value $L$ to
\textit{lifter} the cepstra according to the following formula
\hequation{
  {c^{\prime}}_n = \left( 1 + \frac{L}{2} sin \frac{\pi n}{L}
      \right) c_n
}{ceplifter}

As an example, the following configuration parameters would
use a 14'th order linear prediction analysis to
generate 12 liftered LP cepstra per target vector
\begin{verbatim}
    TARGETKIND = LPCEPSTRA
    LPCORDER = 14
    NUMCEPS = 12
    CEPLIFTER = 22
\end{verbatim}
These are typical of the values needed to generate a good front-end
parameterisation for a speech recogniser based on linear prediction.
\index{cepstral analysis!LPC based}\index{cepstral analysis!liftering coefficient}

Finally, note that the conversions supported by \HTK\ are not limited to
the case where the source is a waveform.  \HTK\ can convert any
LP-based parameter into any other LP-based parameter.

\mysect{Filterbank Analysis}{fbankanal}

The human ear resolves frequencies non-linearly across the audio spectrum and
empirical evidence suggests that designing a front-end to operate in a similar
non-linear manner improves recognition performance.  A popular alternative to
linear prediction based analysis is therefore filterbank analysis since this
provides a much more straightforward route to obtaining the desired non-linear
frequency resolution.  However, filterbank amplitudes are highly correlated and
hence, the use of a cepstral transformation in this case is virtually mandatory
if the data is to be used in a HMM based recogniser with diagonal covariances.
\index{cepstral analysis!filter bank} \index{speech input!filter bank}

\HTK\ provides a simple Fourier transform based filterbank designed to
give approximately equal resolution on a mel-scale.  Fig.~\href{f:melfbank}
illustrates the general form of this filterbank.    As can be seen,
the filters used are triangular and they are equally spaced along the mel-scale
which is defined by
\hequation{
   \mbox{Mel}(f) = 2595 \log_{10}(1 + \frac{f}{700})
}{melscale}
To implement this filterbank, the window of speech data is
transformed\index{mel scale} using a Fourier transform and the magnitude is
taken.  The magnitude coefficients are then \textit{binned} by correlating them
with each triangular filter.  Here binning means that each FFT magnitude
coefficient is multiplied by the corresponding filter gain and the results
accumulated.  Thus, each bin holds a weighted sum representing the spectral
magnitude in that filterbank channel.\index{binning} As an alternative, the
Boolean configuration parameter
\texttt{USEPOWER}\index{usepower@\texttt{USEPOWER}} can be set true to use the
power rather than the magnitude of the Fourier transform in the binning
process.  \index{cepstral analysis!power vs magnitude}

\centrefig{melfbank}{110}{Mel-Scale Filter Bank}

\index{speech input!bandpass filtering}
Normally the triangular filters are spread over the whole frequency range from
zero upto the Nyquist frequency.  However, band-limiting is often useful to
reject unwanted frequencies or avoid allocating filters to frequency regions in
which there is no useful signal energy.  For filterbank analysis only, lower
and upper frequency cut-offs can be set using the configuration parameters
\texttt{LOFREQ}\index{lofreq@\texttt{LOFREQ}} and
\texttt{HIFREQ}\index{hifreq@\texttt{HIFREQ}}. For example,
\begin{verbatim}
    LOFREQ = 300
    HIFREQ = 3400
\end{verbatim}
might be used for processing telephone speech.  When low and high pass cut-offs
are set in this way, the specified number of filterbank channels are distributed