book2

Best algorithm for LZW ..C language

It has a rich spectrum of harmonics,
decaying at around 12\ dB/octave, and each harmonic is affected
by the vocal tract resonances.
.rh "Vocal tract resonances."
A simple model of the vocal tract is an organ-pipe-like cylindrical tube
(Figure 2.1),
with a sound source at one end (the larynx) and open at the other (the lips).
.FC "Figure 2.1"
This has resonances at wavelengths $4L$, $4L/3$, $4L/5$, ..., where $L$
is the length of the tube;
and these correspond to frequencies $c/4L$, $3c/4L$, $5c/4L$, ...\ Hz, $c$
being the speed of
sound in air.
Calculating these frequencies, using a typical figure for the
distance between larynx and lips of 17\ cm,
and $c = 340$\ m/s for the speed of sound, leads to resonances at
approximately 500\ Hz, 1500\ Hz, 2500\ Hz, ... .
.pp
When excited by the harmonic-rich waveform of the larynx,
the vocal tract resonances produce
peaks known as
.ul
formants
in the energy spectrum of the speech wave (Figure 2.2).
.FC "Figure 2.2"
The lowest formant, called formant one, varies from around 200\ Hz
to 1000\ Hz during speech, the exact range depending on the size
of the vocal tract.
Formant two varies from around 500 to 2500\ Hz, and formant three
from around 1500 to 3500\ Hz.
.pp
You can easily hear the lowest formant by whispering the vowels in
the words "heed", "hid", "head", "had", "hod", "hawed", and "who'd".
They appear to have a steadily descending pitch, yet since you are
whispering there is no fundamental frequency.
What you hear is the lowest resonance of the vocal tract \(em formant one.
Some masochistic people can play simple tunes with this formant by putting
their mouth in successive vowel shapes and knocking the top of their head
with their knuckles \(em hard!
.pp
A difficulty occurs when trying to identify the lower formants for speakers
with high-pitched voices.
When a formant frequency falls below the fundamental excitation frequency
of the voice, its effect is diminished \(em although it is still present.
The vibrato used by opera singers provides a very low-frequency excitation
(at the vibrato rate) which helps to illuminate the lower formants even
when the pitch of the voice is very high.
.pp
Of course, speech is not a static phenomenon.
The organ-pipe model describes the speech spectrum during a continuously
held vowel with the mouth in a neutral position such as for "aaah".
But in real speech the tongue and lips are in continuous motion,
altering the shape of the vocal tract and hence the positions of the resonances.
It is as if the organ-pipe were being squeezed and expanded in
different places all the time.
Say
.ul
ee
as in "heed" and feel how close your tongue is to the roof of your mouth,
causing a constriction near the front of the vocal cavity.
.pp
Linguists and speech engineers use a special frequency analyser called a
"sound spectrograph" to make a three-dimensional plot of the variation
of the speech energy spectrum with time.
Figure 2.3 shows a spectrogram of the
utterance "go away".
.FC "Figure 2.3"
Frequency is given on the vertical axis,
and bands are shown at the beginning to indicate the scale.
Time is plotted horizontally,
and energy is given by the darkness of any particular area.
The lower few formants can be seen as dark bands extending horizontally,
and they are in continuous motion.
In the neutral first vowel of "away", the formant frequencies
pass through
approximately the 500\ Hz, 1500\ Hz, and 2500\ Hz that we calculated earlier.
(In fact, formants two and three are somewhat lower than these values.)
.pp
The
fine vertical striations in the spectrogram correspond to single openings of the vocal cords.
Pitch changes continuously throughout an utterance,
and this can be seen on the spectrogram by the differences in spacing
of the striations.
Pitch change, or
.ul
intonation,
is singularly important in
lending naturalness to speech.
.pp
On a spectrogram, a continuously held vowel shows up as a static energy spectrum.
But beware \(em what we call a vowel in everyday language is not the same thing as a
"vowel" in phonetic terms.
Say "I" and feel how the tongue moves continuously while you're speaking.
Technically, this is a
.ul
diphthong
or slide between two vowel positions,
and not a single vowel.
If you say
.ul
ar
as in "hard",
and change slowly to
.ul
ee
as in "heed", you will obtain a diphthong not unlike that in "I".
And there are many more phonetically different vowel sounds
than the a, e, i, o, and u that we normally think of.
The words "hood" and "mood" have different vowels, for example, as do "head" and "mead".
The principal acoustic difference between the various vowel sounds
is in the frequencies of the first two formants.
.pp
A further complication is introduced by the nasal tract.  This is
a large cavity which is coupled to the oral tract by a passage at the
back of the mouth.
The passage is guarded by a flap of skin called the "velum".
You know about this because inadvertent opening of the velum while
swallowing causes food or drink to go up your nose.
The nasal cavity is switched in and out of the vocal tract
by the velum during speech.
It is used for consonants
.ul
m,
.ul
n,
and the
.ul
ng
sound in the word
"singing".
Vowels are frequently nasalized too.
A very effective demonstration of the amount of nasalization in ordinary
speech can be obtained by cutting a nose-shaped hole in a large
baffle which divides a room, speaking normally with one's nose in the hole,
and having someone listen on the other side.
The frequency of occurrence of
nasal sounds, and the volume of sound that is emitted
through the nose, are both surprisingly large.
Interestingly enough, when we say in conversation that someone sounds
"nasal", we usually mean "non-nasal".  When the nasal passages are
blocked by a cold, nasal sounds are missing \(em
.ul
n\c
\&'s turn into
.ul
d\c
\&'s,
and
.ul
m\c
\&'s to
.ul
b\c
\&'s.
.pp
When the nasal cavity is switched in to the vocal tract, it introduces
formant resonances, just as the oral cavity does.
Although we cannot
alter the shape of the nasal tract significantly, the nasal formant
pattern is not fixed, because the oral tract does play a part in nasal
resonances.
If you say
.ul
m,
.ul
n,
and
.ul
ng
continuously, you can hear the difference and feel how it is produced by
altering the combined nasal/oral tract resonances with your tongue position.
The nasal cavity operates in parallel with
the oral one:  this causes the two resonance patterns to be summed
together, with resulting complications which will be discussed in Chapter 5.
.rh "Sound sources."
Speech involves sounds other than those caused by regular vibration of
the larynx.
When you whisper, the folds of the larynx are held slightly
apart so that the air passing between them becomes turbulent, causing a noisy excitation
of the resonant cavity.
The formant peaks are still present, superimposed on the noise.  Such
"aspirated" sounds occur in the
.ul
h
of "hello", and for a very short time
after the lips are opened at the beginning of "pit".
.pp
Constrictions made in the mouth produce hissy noises such as
.ul
ss,
.ul
sh,
and
.ul
f.
For example, in
.ul
ss
the tip of the tongue is high up,
very close to the roof of the mouth.
Turbulent air passing through this constriction causes a
random noise excitation, known as "frication".
Actually, the roof of the mouth is quite a complicated object.
You can feel with your tongue a bony hump or ridge just behind the front
teeth, and it is this that forms a constriction with the tongue for
.ul
s.
In
.ul
sh,
the tongue is flattened close to the roof of the mouth slightly farther back,
in a position rather similar to that for
.ul
ee
but with a narrower
constriction,
while
.ul
f
is produced with the upper teeth and lower lip.
Because they are made near the front of the mouth,
the resonances of the vocal tract have little effect on these fricative
sounds.
.pp
To distinguish them from aspiration and frication, the ordinary speech
sounds (like "aaah") which have their source in larynx vibration are
known technically as "voiced".  Aspirated and fricative sounds are called
"unvoiced".  Thus the three different sound types can be classified as
.LB
.NP
voiced
.NP
unvoiced (fricative)
.NP
unvoiced (aspirated).
.LE
Can any of these three types occur together?
It would seem that voicing and aspiration can not, for the former requires
the larynx to be vibrating regularly, but for the latter it must be
generating turbulent noise.
However, there is a condition known technically as "breathy voice"
which occurs when the vocal cords are slightly apart, still vibrating,
but with a large volume of air passing between to create turbulence.
Voicing can easily occur in conjunction with frication.
Corresponding to
.ul
s,
.ul
sh,
and
.ul
f
we get the
.ul
voiced
fricatives
.ul
z,
the sound in the middle of words like "vision" which I will call
.ul
zh,
and
.ul
v.
A simple illustration of voicing is to say "ffffvvvvffff\ ...".
During the voiced part you can feel the larynx vibrations with a finger
on your Adam's apple, and it can be heard quite clearly if you stop up
your ears.
Technically, there is nothing to prevent frication and aspiration
from occurring together \(em they do, for example, when a voiced fricative
is whispered \(em but the combination is not an important one.
.pp
The complicated acoustic effects of noisy excitations in speech can be
seen in the spectrogram in Figure 2.4 of
"high altitude jets whizz past screaming".
.FC "Figure 2.4"
.rh "The source-filter model of speech production."
We have been talking in terms of a sound source (be it voiced or unvoiced)
exciting the resonances of the oral (and possible the nasal) tract.
This model, which is used extensively in speech analysis and synthesis,
is known as
the source-filter model of speech production.  The reason for its success
is that the effect of the resonances can be modelled as a frequency-selective
filter, operating on an input which is the source excitation.
Thus the frequency spectrum of the source is modified by multiplying it
by the frequency characteristic of the filter (or adding it, if amplitudes
are expressed logarithmically).
This can be seen in Figure 2.5, which shows a source
spectrum and filter characteristic which combine to give the overall
spectrum of Figure 2.2.
.FC "Figure 2.5"
.pp
Although, as mentioned above, the various fricatives are not subjected
to the resonances of the vocal tract to the same extent
that voiced and aspirated
sounds are, they can still be modelled as a noise source followed by
a filter to give them their different sound qualities.
.pp
The source-filter model is an oversimplification of the actual speech
production system.  There is inevitably some coupling between the vocal
tract and the lungs, through the glottis, during the period when
it is open.  This effectively makes the filter characteristics
change during each individual cycle of the excitation.
However, although the effect is of interest to speech re