Transcript Speech Science V

WS 2007/8
Speech Science V
Akustische Grundlagen
Recapitulation
• Airstream production (pulmonic, glottal or velaric
airstreams serve as a basis for speech sound
production)
• The kinetic airstream energy can be transformed into
acoustic energy at various points along the vocal tract.
• The first point at which the transformation can occur
is at the glottis (the space between the vocal folds)
• The acoustic energy is periodic if the vocal folds
vibrate, aperiodic if they are constricted but do not
vibrate
Topics
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What are sounds physically?
Periodic signals - sinusoids
Damping - phonation
Complex waveforms
Reading: a) Kent, Ch. 2, 22-34
b) Borden, Harris & Raphael, Ch. 3, 24-44/31-53
Deutsch: c) Pompino-Marschall, Teil II, Ch. 2, 87-101
d) Reetz, Ch. 2, 3-32
Air-particle movement
• Acoustic energy = fluctuating pressure
uniform pressure state (all
particles equidistant
local disturbance moves P1 close
to P2 (local pressure increase)
P2 moves away from P1, thus
moving closer to P3
Condensation & rarifaction
• Pressure changes travel (at the speed of sound!)
The pressure change in one area
is transmitted to the next ….
so the sound moves from its
origin and is heard elsewhere
This process is called
“sound propagation“
Periodic signals
• A disturbed air particle oscillates through its resting
point and back (just like any other vibrating system):
The sinewave
• The oscillations follow a strict pattern which can be
described with a sinusoid function
Calculating the amplitude
• The momentary amplitude D is determined by the
position on the circumference (which is equivalent to
the angle  of the radius line to that point):
D = sin 
or:
D = A sin 2 π t/T
D = A sin Ωt
Ω = 2 π/T
or:
where
= position on the
circumference
of the circle.
(which changes
with time)
Loss of energy (damping)
• Any “real-world“ vibration will die out because of
energy loss (friction)!
The more energy
loss, the more
quickly the signal
dies out (the more
strongly damped
it is)
Logarithmically
and linearly
damped signals
What has this to do with speech?
• The acoustic energy from the vocal-fold vibrations is
strongly damped
• Each glottal closure adds energy to the system, which
quickly weakens.
Negative pressure is
created by the abrupt
closure of the vocal
folds. The oscillation
is visible during the
closed phase, but the
damping is greater in
the open phase
Damped glottal cycles
• Idealized, different degrees of damping would effect
the speech signal as the following figure shows
In both signals the glottal impulse renews the energy after 5 oscillations,
but in the left signal damping is weak and the oscillations have continued
strongly; in the right signal damping is strong and the oscillations have
almost died out.
Complex signals
• What aspect of the glottal signal oscillates (and
is therefore damped)?
• The glottal signal is NOT a single sinusoid
(i.e. not energy at one single frequency)
• When the vocal folds vibrate and come together
(each glottal cycle), they produce an impulse
with harmonic energy
• These “harmonics“ are vibrations at every
multiple of the fundamental glottal frequency
F0 = 100 Hz; Harmonics = 100, 200, 300, 400, 500, 600 ……. Hz
What do complex
signals look like?
At any point in time,
the overall amplitude
(energy) is the sum
of the component
amplitudes
E-synth demo
How complex is the glottal signal?
The glottal flow
signal is like a
rounded sawtooth
wave
This gives a frequency
distribution (spectrum)
with all harmonics of
the fundamental (F0)
present with decreasing
power (-12dB per octave)
Is the glottal signal like a sawtooth?
A square wave has
the odd-numbered
harmonics
The sawtooth wave
has every harmonic
Summary
• Local fluctuations of air pressure (air-particle proximity)
= acoustic energy
• These are propagated at the speed of sound
• Repeated patterns of pressure change are „periodic signals“
• The simplest waveform is the sinusoidal wave, which can
be described with a simple mathematical function
• Complex waves can be described as a sum of simple waves
• The glottal wave is the sum of all the harmonics of the
fundamental frequency
• The glottal wave is very heavily damped; each glottal
closure brings fresh energy into the system.