1. ACOUSTICAL THEORY OF SPEECH PRODUCTION
Robert A. Prosek, Ph.D.
CSD 301

3. Acoustical Theory There is nothing more practical than a good theory
The linear source-filter theory is one of the best in our field
Based on Gunnar Fant’s “Acoustic Theory of Speech Production”
The theory expresses articulatory-acoustic relationships

5. Acoustical Theory The source is vocal fold vibration
for some consonants, the source is more complex
can be in the vocal tract or a combination of both
The filter is the vocal tract
extending from the vocal folds to the lips or nares
like all filters, the vocal tract is frequency dependent

6. Acoustic Theory
The source and the filter are assumed to be independent
this is an assumption made for convenience
it implies that you can change the output of the vocal folds without changing the vocal tract
vice-versa

7. Vowels Modeled as a tube closed at one end and open at the other
the closure is a membrane with a slit in it
the tube has uniform cross sectional area
membrane represents the source of energy (vocal folds)
the energy travels through the tube
the tube generates no energy on its own
the tube represents an important class of resonators
odd quarter length relationship
Fn=(2n-1)c/4l

9. Vowels (2) There are an infinite number of resonances for this tube
we need only consider the first three or four
the model is valid to only about 5 kHz
The model was developed by Chiba and Kajiyama in 1941
based on pipe organs for which a great deal was known

10. Vowels (3) If c=35000 cm/s, and l=17.5 cm
What are the first three resonances?
The simple tube closed at one end and open at the other, with the above length, is a reasonable approximation of /ᴧ/ produced by a male talker

11. Vowels (4) Some points to note:
A curved tube (vocal tract) and a straight tube (model) behave identically acoustically out to 5 kHz
this is because the curve begins to affect acoustic signals with a short wavelength
The resonances are equally spaced if the tube has uniform cross sectional area
Remember: all of the energy comes from the source (vocal fold vibration for vowels)
Changing the length of the tube changes the resonance frequencies
Influenced by age and sex
l= 14.5 cm for females
l= 8.75 cm for children

13. Vowels (5) A one-vowel model isn’t very useful
Different vowels are modeled, acoustically, by different vocal tract shapes
Phonetically, how are vowels distinguished?
If we place a constriction in the tube (vocal tract)
the resonances changes
if you change the articulation, you change the vocal tract shape, and the resonance frequencies, amplitudes and bandwidths

15. Vowels (6) the amplitude of the harmonics decreases by -12 dB/octave
The output energy of a vowel is the product of
the source energy
the size and shape of the resonator
the radiation characteristic
Glottal source characteristics for vowels
vocal fold vibration is periodic
what does this imply for the spectrum?
f0 or F0 is used to indicate the vocal fundamental frequency
the amplitude of the harmonics decreases by -12 dB/octave

20. Vowels (7) Filter characteristics for vowels
the vocal tract is a dynamic filter
it is frequency dependent
it has, theoretically, an infinite number of resonances
each resonance has a center frequency, an amplitude and a bandwidth
for speech, these resonances are called formants
formants are numbered in succession from the lowest
F1, F2, F3, etc.
A1, A2, A3, etc.
B1, B2, B3, etc.
the formants together form the transfer function
input-output relationship
formants become physically evident only when energized

21. Vowels (8) Radiation characteristic
acoustic effect when a sound leaves a small area and enters a large one
The effect is to raise the slope of the spectrum by +6 dB/octave
Acoustic Phonetic Relationships for Vowels
F1 is inversely related to tongue height
F2 is directly related to tongue advancement
Lip rounding lowers all formant frequencies

23. Vowels (9) Perturbation Theory
Volume velocity variations reflect the way air particles vibrate at a particular point in the vocal tract
At some points, vibration is minimal (node); at others, maximal (antinodes)
For F1, the antinode is at the open end and the node is at the closed end
For F2, there are two antinodes and two nodes
For F3, there are three antinodes and three nodes
etc.

24. Vowels (10) Perturbation Theory (continued)
if a change in cross sectional area is applied (a perturbation)
the acoustic effect depends on proximity to a node or an antinode
near an antinode the formant frequency lowers
near a node the formant frequency rises
lip constrictions lower all formant frequencies
laryngeal constrictions raise all formant frequencies

25. Vowels (11) Amplitude relationships
amplitudes depend on formant frequencies
if F1 is lowered (raised), A1 lowers (rises)
if two formant frequencies move closer together, then both peaks increase in amplitude
how do you raise or lower formant frequencies?

26. Vowels (12) Source-Filter Interactions
Some vocal tract shapes may affect vocal fold vibration
Singers’ formant
High impedance constrictions require greater subglottal air pressure
Vocal tract - vocal fold coupling during open phase of vibratory cycle

27. Consonants (1)
The linear source-filter theory can be used to describe the acoustics of consonants as well as vowels
For consonants, however, the source is not always at the level of the vocal folds
some sources are in the vocal tract
these sources are aperiodic
durations and amplitudes also are different from vowels
Nonetheless, source-filter theory gives us a series of expectations for the acoustic characteristics for consonants

28. Consonants (2) Fricatives
Modeled as a tube with a very severe constriction
The air exiting the constriction is turbulent
The Reynold’s number gives the conditions for turbulence
Re=vh/ʊ
Notice that turbulence can be generated in two ways
Zeros or antiformants can be found in the spectrum
Because of the turbulence, there is no periodicity unless accompanied by voicing
What does an aperiodic spectrum look like?

29. Consonants (3) When a fricative constriction is tapered
the back cavity is involved
this resembles a tube closed at both ends
Fn=nc/2l
such a situation occurs primarily for articulation disorders

30. Consonants (4) Nasal consonants
Velopharyngeal port is open and the oral cavity is completely blocked at some point
The side-branch resonator produces antiformants (zeros)
The overall vocal tract is longer than for vowels
What effect does this have on the spectrum?
Oral formants, nasal formants, nasal antiformants
Nasal murmur

31. Consonants (5) Stops The tube model is not altered very much for stops
However, the time domain becomes critical
There is a complete closure of the vocal tract somewhere
Pressure builds up behind the closure
Rapid release
The articulation results in a burst and transitions

32. Consonants (6) Other consonants are variations of these Affricates
Liquids
Glides
Diphthongs