ANALYTICAL DESCRIPTION OF THE PRODUCTION OF

FORMATS IN HUMAN SPEECH

Damyan Damyanov

Technical University of Sofia, Faculty of Automation, Department for Industrial Automation,

Bulgaria, Sofia, Darvenitsa 1756,Bul. Kliment Ohridksi 8, block 9,room 9420

damyan_damyanov@tu-sofia.bg

Keywords: model of speech production, man-machine systems.

Abstract: For the purposes. of speech synthesis, biometrics , medical and psychological diagnosis, the functioning of

the glottis during phonation has been studied many times. At present, a relatively trivial solution proposed

by Fant has established itself, regardless of the actual purpose of the system, using the "pusle source - filter"

model. The model of Fant allows the linear prediction method to perform reconstruction of the current form

of the vocal tract and the excitation of glottal volume velocity. But the practice shows that the fluctuations

of the speech tract due to psycho-physiological effect on the functioning of the facial muscles in most cases

are negligible. Thus, they are below the accuracy, which the linear model allows, using approximation with

a cascade of coaxial cylindrical sections of equal length and constant cross-section. This requires more

complex algorithms, and thus additional information is extracted from the pattern of air volume velocity

after glottis. In this study, it is to be shown, that the model of Fant actually allows depiction of the psycho-

physiological changes in the spectral features of the speech signal without the use of additional models. For

this purpose it is sufficient to analyze the relationships of the main parameters of the excitation pulse of the

source with the frequency response of the filter. In the current practice, these correlations are not considered

and the source and the filter are examined separately.

1 INTRODUCTION

Phonation is a process which takes place in the

middle part of the larynx and sets up vibrations to

the exhaled airstream. As a consequence of this

process the air volume velocity after the glottis

immediately shows vibrational patterns (Figure 1),

which determines the pitch frequency of the speech

signal (Тилков, Д., Бояджиев., Т 1990). Changing

the tension of the vocal folds and the pressure during

the speech production process, one gets the desired

pitch frequency, needed for phonation of vowels and

voiced consonants. In the formation of non-voiced

consonants the vocal folds do not come near each

other and their constellation is like at physiological

breathing (Pickett J.M, 1982). In this case, the

incoming air pressure from the lungs is modulated

by the formation of turbulence and closure of the

vocal tract. The spectra of the resulting sound

sources are modified by resonances, the frequency

of which depends on the time-varying shape of the

throat and mouth, the location of the tongue and

many more.

Modern study of acoustic phenomena in the oral-

pharyngeal tract began in 1941 with the work of

Chiba and Kajiyama (Chiba, T., Kajiyama M.,

1941). The fundament of the present theory and

practice is shaped in 1960 by Fant (Fant, G., 1960),

and others. The systems for processing, transmitting

and storing of speech signals use various methods

and techniques, but they are all based on a model of

the functioning of articulatory tract and the air

volume velocity after the glottis. The purpose of the

modelling process of speech production is not only

to study its properties and specifics, but also to solve

problems for its effective coding and transmission ,

Damyanov D.

ANALYTICAL DESCRIPTION OF THE PRODUCTION OF FORMATS IN HUMAN SPEECH.

DOI: 10.5220/0004785600790084

In Proceedings of the Second International Conference on Telecommunications and Remote Sensing (ICTRS 2013), pages 79-84

ISBN: 978-989-8565-57-0

the automatic synthesis of speech and speech

recognition, for biometrical applications and others.

Figure 1: Air volume velocity immediately after the glottis

for vowels and voiced consonants. Position of the vocal

folds: a - phonation of vowels and voiced consonants, b -

physiological breathing.

In every such model (Proakis, J.,2000), in one

degree of another, the main components of

articulatory tract in terms of the laws of acoustics are

reflected (Figure 2)

Figure 2: Main components of the acoustic articulatory

tract.

These components include the excitation of the

vocal cords, the time-varying shape of the vocal

tract, radiation from the lips etc. Resonant

phenomena in the speech production process are

actually affected by losses in the walls of the tract,

depending on the thermal conductivity, elasticity and

friction. Significant influence is done by the nasal

cavity with the absorption of certain frequency

components of the spectrum (antiresonant

phenomena). This complex nature of the process

allows the development of many models, differing in

structure and degree of relevance. Interestingly,

despite the apparent complexity of the problem, it

found a relatively trivial solution proposed by Fant

(Fant, G., 1960), which has established itself in

practice regardless of the actual purpose of the

system.

The classical model of Fant separates the

excitation from the shaping of individual sound

components of speech, allowing approximately

treatment of speech sounds as a linear system.

Lungs, which provide air volume velocity, are

presented as direct current power source. Their

output is divided, corresponding respectively to the

voiced and unvoiced parts of the signal. The pulse

generator modulates the air volume velocity from

periodical excitation of the vocal folds, and the noise

generator models the formation of turbulence in the

places, where the vocal tract changes its cross-

section. The final speech signal is obtained after the

components are added together and passed through a

filter with linear transfer function, which models the

articulatory tract.

In modern systems, this model has found its

discrete implementation (Figure 3).

Figure 3: Digitalized model of Fant.

Generating a voiced speech segment after the z-

transform of a sampled speech signal is described by

the equation:

() () () ()

Sz U zVzLz

(1)

)(

)()()(

zGzzU

son

−

∞

−

∑

(2)

It is assumed, that the sampling period is T=1,

and the period of the pitch frequency is a multiple of

it Tp = KT (Damyanov, D., Galabov, V., 2012a).

The transfer function of the model of the glottis, the

model of the vocal tract and the lips radiation can be

combined in a common transfer function:

)()()()( zLzVzGzH

(3)

And the speech production process can be

written as

)()()( zHzEzS

(4)

Second International Conference on Telecommunications and Remote Sensing

{}

nTt

tsnTsnTsZzS

== )()(,)()(

(5)

Where E(z) is the z-transformed pulse excitation

of the glottis. Adoption of certain hypothesis about

the spectral properties of the glottis, of the vocal

tract and the lips radiation (Fant, G., 1960) allows

the use of an all-pole filter:

∑

−

)(

(6)

Finding the coefficients of this filter is a task,

successfully solved in theory and practice. (Proakis,

J.,2000, Trashlieva, V., Puleva, T., 2011)

2 MOTIVATION

Using a process of speech production of type source-

filter, based on the model of Fant, many of the tasks,

associated with the processing of speech signals are

successfully solved. In this study, it is to be shown,

that despite their simplicity, these models are able to

explain some phenomena of the speech production,

observed in the changes of current psycho-

physiological state of humans. These include

changed rations of the amplitudes of formant

frequencies (less harsh or ringing voice), impaired

understandability, etc. For their description and

analysis of the functioning of the glottis during

phonation has been studied many times, in order to

create relevant model, especially for the purposes of

speech synthesis, medical and psychological

diagnosis, and biometrics. Much of the testing

methods are borrowed from medicine in order to

achieve greater accuracy, or to make measuring

easier. All of the above methods do not work

directly with the desired variable, but with some

other, depending on the desired one. Given the

complexity of making laryngoscopic and

laryngoendoscopic studies, and especially the need

for medical intervention, and because of the

significant impact of these methods on the overall

process of speech production, a great number of

indirect methods have been developed. These

include methods, base on electromyography -

registering the signals of muscle activity in the

throat while speaking, glottography - working with

the impedance of the neck in the plane of the glottis,

which largely depends on the cross-section of the air

volume velocity after the glottis. Despite numerous

studies, currently there is no unified theory that

explains the process of these changes in the spectral

characteristics of the speech signal. Most authors

seek the cause of these phenomena in the psycho-

physiological change in current form of the

articulatory tract. The model of Fant allows the

linear prediction method to perform reconstruction

(with some degree of approximation) of the current

form of the tract and the excitation of acoustic

volume velocity after the glottis. It is expected, that

the modelling of the speech tract provides conditions

for obtaining relevant information about the

functioning of the facial muscles and the

corresponding parts of the nervous system, which

are extremely sensitive to current psycho-

physiological state of the individual (Ekman, P,

Friesen, W., 1978 ). But the practice shows, that the

fluctuations of the speech tract due to psycho-

physiological effect on the functioning of the facial

muscles in most cases are too small . Thus they are

below the accuracy, which the linear model allows,

using approximation with a cascade of coaxial

cylindrical sections of equal length and constant

cross-section (Pfister, B., Kaufmann, T., 2008).

This requires more complex algorithms and

thus additional information is extracted from the

pattern of air volume velocity after glottis. The air

volume velocity gives information about the current

psycho-physiological condition in two ways - first,

through the entire process of speech production,

concerning the higher nervous activity, and the

second by the functional state of the autonomic

nervous system, including the overall muscular

tonus (Reuter-Lorenz, Patricia A., et.al., 2010, Kalat,

James W. 2012). For the extraction of this

information, the use of relatively complex models is

required, describing the tension on the vocal folds,

the mechanism of stretching and vibrating, the

pressure of the incoming air flow from the lungs,

etc. In this study, it is to be shown, that the model of

Fant actually allows depiction of the psycho-

physiological changes in the spectral features of the

speech signal without the use of additional models.

For this purpose, it is sufficient to analyze the

relationships of the main parameters of the

excitation pulse of the source with the frequency

response of the filter. In the current practice, these

correlations are not considered and the source and

the filter are examined separately. For readability

purposes, the following simplifications will be made

that do not change the generality of the study:

• The influence of the transfer function of

the glottis and the lips radiation will be

neglected, since they don't affect the

Analytical Description of the Production of Formats in Human Speech

formant frequencies, but only their

decay ;

• The excitation of the source will be

considered as a sequence of rectangular

pulses;

• The attenuation of formant frequencies

will be ignored, i.e. poles of the filter of

the vocal tract will lie of the unit circle;

3 PRODUCTION OF FORMANTS

IN HUMAN SPEECH

In this study, it is assumed, that the model of the

vocal tract is of second order:

)(

(7)

i.e. the signal will contain only one formant with

circular frequency

. The excitation pulses are of

type (Damyanov, D., Galabov, V., 2012b):

1,1

)1(,0

)1()1(,1

)(

−=

<≤−+

−+<≤−

⎪

⎩

⎪

⎨

⎧

imp

ggglottisopen

gglottisopeng

mTtTmt

TmttTm

(8)

where

is the period of the pitch frequency , and

glottisopen

is the duration of the phase of open

glottis. The output signal for the period of the pitch

frequency (m=1) is:

)

(

)(

sin

glottisopen

AOt

glottisopen

ϕω

+−=

(9)

for

glottisopen

, i.e. in the phase of open

glottis, and:

)

(

)(

sin

glottisclosed

ϕω

(10)

for

glottisopen

≥

, i.e. in the phase of closed

glottis, where:

glottisopen

AO =

is the DC component of the

signal in the phase of open glottis

glottisopen

A =

and

)

(

sin

glottisopen

glottisclosed

are the

amplitudes of the signal in the phases of open and

closed glottis

glottisopen

and

glottisopen

glottisclosed

πϕ

−=

are the

angular phases of the signal in the phases of open

and closed glottis

2 f

are the circular frequency, which

corresponds to the formant frequency

We can observe the following important features:

 In the two phases - of open and closed glottis

- the formant frequency is determined only

on the coefficient of plain gain of the filter

 The amplitude of the signal in the phase of

closed glottis depends again on this

coefficient, but also in a complicated way

on the ratio of duration of the preceding

phase of open glottis to the period of the

formant frequency.

 The phase shift of the signal depends in a

similar way on the above stated variables.

Practically, this means that without changes in

the filter parameters, i.e. the geometry of the vocal

tract, changes in length of the phase of open glottis

can increase or decrease the formant frequencies of

the speech signal (Damyanov, D., Galabov, V.,

2012a). For better understanding of the paradigm, a

dimensionless coefficient is introduced, which is

proportional to the duration of the phase of open

glottis to the period of the formant frequency:

glottisopen

(11)

In terms of amplitude of the signal before and

after closure of the glottis the coefficient can be

defined:

glottisclosed

glottisopen

glottisclosed

glottisopen

(12)

where the

glottisopen

glottisclosed

−

is the

duration of the phase of closed glottis during the

period of the pitch frequency (Damyanov, D.,

Galabov, V., 2012b). The functional relationship

between these two coefficients is:

Second International Conference on Telecommunications and Remote Sensing

)

sin

glottisopen

glottisclosed

glottisopen

⎟

⎠

⎞

⎜

⎝

⎛

(13)

It can be seen, that varying the duration of the

phase of open glottis, without changing the filter

parameters, i.e. the geometry of the vocal tract, for a

given amplitude of the generated signal in the phase

of closed glottis can take any value from zero to two

times the amplitude in the phase of open glottis

(Damyanov, D., Galabov, V., 2012c).

This effect becomes more interesting, if the

speech segment contains several periods of the pitch

frequency. Then, besides the coefficient

glottisopen

, the ratio of the

amplitudes will be affected by the ratio of the length

phase of closed glottis during the period of pitch

frequency:

glottisopen

impfull

(14)

In this case one can obtain relatively complex

analytical dependencies. For example the

relationship of the amplitudes of the signal in the

phase of closed glottis to the phase of open glottis in

the second period of the pitch frequency is given by

⎥

⎦

⎤

⎢

⎣

⎡

)

cos()

sin(

)

(

impfull

glottisopen

glottisclosed

glottisopen

ωω

(15)

)

sin(

)

(

sin

)

2sin(

)

sin(

−

⎥

⎦

⎤

⎢

⎣

⎡

⎟

⎠

⎞

⎜

⎝

⎛

−+−

⎟

⎠

⎞

⎜

⎝

⎛

−+

ωω

impfull

glottisopen

impfull

glottisopen

If we assume that:

Nofonpresentatibinarythefrom

bitsofnumbertotalnumbits =

(16)

Then, for the N-th period of the pitch frequency

the dependencies are as follows:

⎪

⎭

⎪

⎬

⎫

⎪

⎩

⎪

⎨

⎧

+−+−+

+−

∑

∏

∑

+−

−

BSBBBS

impfull

BFBBSB

impfull

glottisclosed

numbits

numbitssab

sabsub

sabsab

glottisopen

numbits

sab

ampl

glottisopen

numbits

sab

numbits

glottisopen

))))(

222(1(

sin(

))2

cos(2(

))22

sin(

)

sin(2

101

)3(

(17)

where

⎪

⎩

⎪

⎨

⎧

−

else

equalis

Nofonpresentatibinarythefrom

bittsignificanthsabtheif

BSB

(18)

⎪

⎩

⎪

⎨

⎧

else

equalis

Nofonpresentatibinarythefrom

bitfirsttheif

BFB

(19)

⎪

⎩

⎪

⎨

⎧

−

else

equalis

Nofonpresentatibinarythefrom

bittsignificansubthef

BSS

(20)

⎩

⎨

⎧

−−+

elsesabnumbitsBSB

numbitssabifBSS

BBS

(21)

and

)

sin(

))1((

+−−

−+=

impfull

glottisclosed

glottisopen

(22)

One can make the following conclusion:

By changing the ratio of the duration of the

phase of close glottis to the length of the pitch

frequency and without changing the geometry of the

vocal tract, one can generate speech segments, in

which the formant amplitude for each subsequent

period increases, decreases, or does not change

much. This can be seen in the two parts of figure 4.

In the figure, a speech signal, generated with the

model of Fant is resented. It contains one formant,

which has frequency 420 Hz. The pitch is 199 Hz,

and the plot contains 9 pitch periods. The signal in

the first part has

glottisopen

t 39

, and the

second part has

glottisopen

t 25

Analytical Description of the Production of Formats in Human Speech

4 CONCLUSIONS

The study shows that the model of Fant adequately

describes many phenomena of the speech production

process, that are known form theory and practice.

The reason for this probably lies in the genesis of the

model. A "pulse source-filter" model is created for

simplification of the process of analysis and

parameterization of a specific implementation. This

is accomplished, with the assumption, that the filter

is practically independent of the source of excitation.

This allows the implementation of effective methods

and techniques for the evaluation of the filter. This

approach gives excellent results in most cases -

mainly in speech analysis, synthesis, coding and

transmission. When the speech signals are used for

medical, psycho-physiological, biometrical purposes

however, it is customary to consider that the model

of Fant is not sufficiently relevant. This requires the

use of much more complex models and additional

information sources. Recently, the problem becomes

even more acute with the ever increasing demands

on quality of processing and transmission of speech

signals and their use in mobile devices. This paper

shows, that the model can be made much more

efficient without further complication. This is

achieved, using the cumulative effect of some of the

processes, that can be found in source and in the

filter.

Figure 4: Speech signal, generated with the model of Fant,

containing one formant, with pitch 199 Hz, 9 pitch

periods, with formant frequency 420 Hz, and duration of

the phase of open glottis 39 ms for a) and 25 ms for b).

REFERENCES

Chiba, T., Kajiyama, M.1995,The vowel, Its Nature and

Structure. Tokyo-Kaiseikan, Tokyo 1995

Damyanov, D., Galabov, V., 2012a, Characteristics of the

model of Fant of second order on speech production,

Proceedings of the Technical University - Sofia,

Volume 62, Issue 2, pp. 181-188, ISSN 1311-0829 ,

Sofia, 2012,

Damyanov, D., Galabov, V., 2012b, On the Impact of

duration of the phase of open glottis on the spectral

characteristics of the phonation process, Proceedings

of the Technical University - Sofia, Volume 62, Issue

2, pp. 173-180, ISSN 1311-0829 , Sofia, 2012,

Damyanov, D., Galabov, V., 2012c, Some effects of the

assumption of an all-pole filter, used to describe

processes of type "pulse source, 1-st International

Conference on Telecommunications and Remote

Sensing, August, 29-30, pp. 139-145, ISBN 978-989-

8565-28-0 , Sofia, 2012,

Ekman, P., Friesen W., 1978, The Facial Action Coding

System, Consulting Psychologist Press, San Francisco.

CA, 1978

Fant, G., 1990, Acoustic Theory of Speech Production,

Mouton&Co, Hauge

Flannagan, J., 1992, Speech analysis, Synthesis and

Perception, Springer, Berlin, 1992

Hayes, M., 1999, Schaum's Outline of Theory and

Problems of Digital Signal Processing, Singapore,

McGraw-Hill, 1999

Kalat, James W. 2012, Biological Psychology, Wadswoth.

Cengage Learning, 10-th edition, Belmont, 2009

Pfister, B., Kaufmann, T., 2008, Sprachverarbeitung -

Grundlagen und Methoden der Sprachsynthese und

Spracherkennung, Springer Verlag, Heidelberg, 2008

Pickett, J.M. 1982, The sounds of speech communication ,

Univercity Park Press, Baltimore, 1982

Proakis, J.,2000, Discrete Time Processing of Speech

Signals, New Jersey, JohnWiley&Sons, IEEE Press,

2000

Rabiner, L., Schafer R. 1992, Digital processing of speech

signals, Prentice-Hall Inc, Engelwood Cliffs, New

Jersey, 1992

Reuter-Lorenz, Patricia A., et.al., 2010, The Cognitive

neuroscience of mind: A tribute to Michael S.

Gazzaniga, MIT Press, April, London, 2010

Trashlieva, V., Puleva, T., 2011, Model building for

optimal administrative process management,

International Conference Automatics and

Informatics'11, Bulgaria, 3-7.10.2011, pp B-263-B-

266, ISSN 1313-1850, Sofia, 2011

Тилков, Д., Бояджиев., Т 1990, Българска Фонетика,

Наука и изкуство София 1990

Second International Conference on Telecommunications and Remote Sensing