VOICE SIGNALS CHARACTERIZATION THROUGH ENTROPY

MEASURES

Paulo Rog

erio Scalassara, Mar

ıa Eugenia Dajer, Carlos Dias Maciel and Jos

e Carlos Pereira

School of Engineering of S

ao Carlos, University of S

ao Paulo, Avenida Trabalhador S

ao-carlense, 400, S

ao Carlos, Brazil

Keywords:

Voice, entropy, phase space reconstruction, nodule, predictability.

Abstract:

Human voice has been a matter of interest for different areas as technological development and medical sci-

ences. In order to understand the dynamic complexity of healthy and pathologic voice, researchers have

developed tools and methods for analysis. Recently nonlinear dynamics has shown the possibility to explore

the dynamic nature of voice signals from a different point of view. The purpose of this paper is to apply en-

tropy measures and phase space reconstruction technique to characterize healthy and nodule affected voices.

Two groups of samples were used, one from healthy individuals and the other from people with nodule in

the vocal fold. They are recordings of sustained vowel /a/ from Brazilian Portuguese. The paper shows that

nonlinear dynamical methods seem to be a suitable technique for voice signal analysis, due to the chaotic

component of the human voice. Since the nodule pathology is characterized by an increase in the signal’s

complexity and unpredictability, measures of entropy are well suited due to its sensibility to uncertainty. The

results showed that the nodule group had a higher entropy values. This suggests that these techniques may

improve and complement the recent voice analysis methods available for clinicians.

1 INTRODUCTION

The human voice is one of the principal means of

communication, and the acoustic signal carries signif-

icant information about some individual characteris-

tics. The complex normal or pathologic voice produc-

tion mechanism involves different variables. Vocal

fold biomechanics in association with aerodynamic

variables play an important role in voice production

and they are linked to the voice quality changes.

In order to study normal voice and the different

voice disorders, scientists from diverse areas devel-

oped several methods and tools for measurement, di-

agnosis and voice treatment. Therefore traditional

acoustic analysis is an essential and familiar tool for

physicians and speech therapists.

Traditionally, voice has been modeled as a linear

process and acoustic analysis tools are based in lin-

ear system theory. Acoustic parameters evaluate per-

turbation or noise contents in the voice signal. The

classical perturbation parameters evaluate jitter (fun-

damental frequency variation), and shimmer (ampli-

tude variation). Two parameters used to determine the

voice signal noise quantity are the deterministic Har-

monic to Noise Ratio (HNR) and the Coefﬁcient of

Excess (EX) that evaluate the noise from a statistical

point of view (Davis, 1979).

Another interesting parameter is the pitch ampli-

tude (PA), which is a normalized measure of the am-

plitude of the pitch period peak of the residue sig-

nal autocorrelation function. It has a high value for

healthy vowel signals that have clearly deﬁned pitch

period. However, for breathy pathological voices, the

PA is low because the signals have weak periodicity

(Davis, 1979).

Although, these linear tools have been used over

the years, they are based in the assumption that voice

is a linear phenomenon. But, voice production is

a complex mechanism that involves different vari-

ables and exhibits nonlinearities (Kumar and Mul-

lick, 1996). Considering human voice production

(healthy and pathologic) as a nonlinear system, it can

be described by a number of observable output states.

Therefore it can be used in the construction of a state

163

Rogério Scalassara P., Eugenia Dajer M., Dias Maciel C. and Carlos Pereira J. (2008).

VOICE SIGNALS CHARACTERIZATION THROUGH ENTROPY MEASURES.

In Proceedings of the First International Conference on Bio-inspired Systems and Signal Processing, pages 163-170

DOI: 10.5220/0001065401630170

 SciTePress

space description of the system behavior. Voice sig-

nal, as a time series data, makes available the study of

an underlying dynamic and provide the necessary in-

formation to obtain a reconstruction of the state space

behavior of the system. Thus, phase space reconstruc-

tion technique can be used for voice characterization.

Nowadays, the use of entropy measures is

widespread in many ﬁelds of science, whether ap-

plied to stochastic processes or dynamical systems.

As presented by (Amig

o et al., 2007), the applica-

tion of entropy to discrete phase space is very natu-

ral, since its concept has been extended from deter-

ministic continuous dynamics to stationary random

processes and discrete dynamical systems. (Amig

et al., 2007) present a quantity called discrete entropy

to deal with ﬁnite-state systems. This quantity asymp-

totically converges to conventional entropy, as evi-

denced by several examples.

As an example of the applicability of entropy,

(Kirk and Jenkins, 2004) show that the Kolmogorov

entropy is used to investigate software metrics, allow-

ing early assessment of the design quality of software

project. Also, in (Lake et al., 2002), an entropy mea-

sure called sample entropy was proposed. The objec-

tive was to improve the diagnosis of neonatal sepsis

by monitoring the heart rate characteristics. The rate

variability is interpreted as changes in the complex-

ity of the underlying physiological processes. De-

spite the fact the method showed sensitivity to other

signal’s parameters, the results were interesting and

could be used for monitoring at-risk infants.

Measures of entropy are intimately related to the

predictability of signals. These measures can be used

to evaluate forecast skill of a system. According to

(Kleeman, 2002), some progress has occurred in us-

ing processes ensemble spread as an indicator of pre-

dictability. This is formalized in a parameter called

predictive power (Schneider and Grifﬁes, 1999).

Natural processes seem to be unpredictable due

to several reasons, as described in (Crutchﬁeld and

Feldman, 2003). The most important reasons are:

unknown rules that govern the system, existence

of intrinsic mechanisms that amplify ﬂuctuations,

observer-induced sources of randomness, insufﬁcient

volume of data, and, perhaps, the dynamics is too

complicated to have predictions evaluated.

Since the presence of pathologies on the vocal

folds results in behavior change of the voice produc-

tion system, the produced signals are going to be less

predictable than the healthy ones. This work aims to

try to detect these changes using simple entropy mea-

sures to differentiate two kinds of signals: healthy and

pathological. For this paper, the pathology studied is

the presence of nodule in the vocal folds.

In Theory a brief description of the entropy es-

timation is presented and also an explanation about

the vocal fold nodule pathology. In Materials and

Methods the voice samples used in the study are de-

scribed in some details. After that, the phase space re-

construction and entropy estimation methods are pre-

sented. Also, a small discussion is made about the

voice samples’ processing. In Results examples of

signals’ phase space analysis are shown with the gen-

eral results of entropy measures. In Conclusion the

ﬁnal comments about the work is presented.

2 THEORY

In this section a brief explanation of the entropy the-

ory is presented. Also, a description of vocal fold

nodules is shown.

2.1 Entropy

According to (Cover and Thomas, 1991), entropy is a

quantity deﬁned for any probability distribution with

properties that agree with the intuitive notion of infor-

mation measures.

One of the entropy’s ﬁrst concepts was presented

in (Shannon, 1948) as the deﬁnition of a measure of

uncertainty of a random variable. Considering a ran-

dom variable X that assumes values x ∈ χ where χ is

a ﬁnite set, the entropy H(X) can be deﬁned by Equa-

tion (1), with units in bits.

H(X ) = −

∑

x∈χ

p(x)log

p(x) (1)

The probability of x, Pr{X = x}, is denoted by p(x).

If p(x) = 0, p(x)log

p(x) = 0 by convention. This

quantity is dependent on the distribution of X instead

of the actual values of the random variable. As dis-

cussed in (Crutchﬁeld and Feldman, 2003), the en-

tropy measures the average amount of bits necessary

to store outcomes of the random variable.

2.2 Vocal Fold Nodules

Individuals with vocal nodules constitute a large part

of the client population at voice clinics (Colton and

Casper, 1996). They are commonly seen in women,

children, salesmen, and teachers who have to use their

voice too frequently. The main symptoms are hoarse-

ness, breathiness, easy vocal fatigue, and throat dis-

comfort. The voice is better in the morning and wors-

ens in the afternoon after voice use (Fisher, 1996).

The vocal nodule is as a benign lesion occurring

on both sides of the vocal folds, strictly symmetric on

BIOSIGNALS 2008 - International Conference on Bio-inspired Systems and Signal Processing

164

the border of the anterior and middle third of the vo-

cal fold and usually immobile during phonation. The

lesion is conﬁned to the superﬁcial layer of the lamina

propria (Rosen and Murry, 2000; Hirano, 1991).

The vocal folds are subject to several forms of me-

chanical stress during phonation. Vocal fold vibration

during phonation leads to impact stress during colli-

sion between the left and right vocal fold surfaces.

According to different studies, nodules mostly occur

at the midpoint of the membranous vocal folds, where

impact forces are the largest and they are mostly bi-

lateral (Titze, 1994; Jiang and Titze, 1994).

During the closing phase of the folds’ vibration,

the presence of nodules on the outer layer of vo-

cal folds’ tissue inhibits them from being completely

folded on each other. Consequently the glottis clo-

sure is uncompleted, adding turbulent air to the voice

signal. In order to reduce this effect, the subject in-

creases the muscle tension and the subglottal pres-

sure, consequently rising the vocal fold collision

forces (Hillman et al., 1990).

Nodule voice shows perceptually strained/pressed

voice quality and breathiness with various degrees of

turbulent noise. Frequently, the voice also presents

vibrations irregularities, such as roughness and insta-

bility, as well as vocal fry/creak (Hammarberg, 1998).

The nodules are responsible for pitch frequency

and air ﬂow volume changes, also amplitude and mu-

cosal wave reduction and the noise-like turbulence

of airﬂow in the vocal folds. This is mainly due

to the incomplete closure of the vocal folds, glottal

air leakage, and their asymmetrical vibration because

of their biomechanical parameter alterations (Hugh-

Munier et al., 1997).

3 MATERIALS AND METHODS

In this section the voice samples are addressed show-

ing the groups and acquisition method. After that, the

phase space reconstruction technique and the entropy

estimation method are presented. Finally, the voice

signals’ analysis method is shown.

3.1 Voice Samples

For this study, 28 voice signals divided in two equal

groups were used. The ﬁrst group was composed of

healthy people with no voice complaints or laryngeal

pathology. The second group was composed of peo-

ple with vocal fold nodules in different stages of dis-

ease evolution according to (Scalassara et al., 2007).

These voice signals are part of a voice database of

the Group of Bioengineering of the School of Engi-

neering of S

ao Carlos at the University of S

ao Paulo,

Brazil. These signals were collected along the past ten

years and used in several studies (Rosa et al., 2000;

Dajer et al., 2005).

All volunteers were diagnosed by physicians of

the Otolaryngology sector and the Head and Neck

Surgery sector of the Clinical Hospital in the Fac-

ulty of Medicine at Ribeir

ao Preto, Brazil (http:

//www.hcrp.fmrp.usp.br) by means of video-

laryngoscope and stroboscope light.

The data recording was performed using a proto-

col similar to the one presented in (Uloza et al., 2005).

The subjects were asked to produce a sustained vowel

/a/ at a comfortable pitch and loudness level for about

3 seconds. The used microphone was in accordance

to the standards established in Brazil. It was placed at

a distance of 5 cm from the person’s mouth. Consec-

utive trials were performed, selecting the signal with

less voice variability.

As presented in (Davis, 1979), vowel sounds are

generally used in studies of pathological speech be-

cause the vocal folds are vibrating during vowel

phonation. Also, acoustics assessment of laryngeal

function relates to adequacy of sustained vocal fold

vibration. Therefore, in order to collect the data,

the sustained /a/ phoneme was used to evaluate the

acoustical parameters of the samples. In English, this

phoneme is equivalent to “a” in “dogma”.

At voice acquisition, it was necessary to check if

the individual could cope with the phonation interval

and, in negative case, he was asked to stop uttering.

This procedure was important because the mainte-

nance of the utterance causes an increase of the voice

fundamental frequency and an artiﬁcial stability on its

production (Rosa et al., 2000). In order to avoid the

inﬂuence of transitory phenomena, the start and end-

ing of the acquired voice signal were discarded. Then,

it was possible to ensure that the beginning and end-

ing of voicing did not inﬂuence the ﬁnal result.

After that, the amplitude of the signal was normal-

ized according to its absolute maximum value. It was

necessary to eliminate the inﬂuence of different sound

levels from the signals collected. All voices samples

were quantized in amplitude with 16 bits and recorded

in mono-channel WAV format to preserve the ﬁdelity

of the signal. The sampling frequency was 22050 Hz.

3.2 Phase Space Reconstruction

Technique

In order to describe the nonlinear dynamic character-

istics of voice signals, sustained vowel data set was

analyzed with ANL (An

alise N

ao-Linear) software

VOICE SIGNALS CHARACTERIZATION THROUGH ENTROPY MEASURES

165

(Dajer et al., 2005). This piece of software was devel-

oped using Matlab 7.0 and the Tisean Package (Heg-

ger et al., 1999; Kantz and Schreiber, 2004). The

ANL is based in the phase space reconstruction tech-

nique and represent the vocal folds vibration as an or-

bit trajectory in phase space with time evolution.

The voice signal can be represented by the time

series x(t

), t

= t

+ iT , with i = 1,2,. .. ,N, where

N is the length of the signal and T is the sampling

period (Rabiner and Schafer, 1978). The phase space

reconstruction of this signal is performed by plotting

the time series x(t

) against itself at some time delay

(Ott et al., 1994; Packard et al., 1980).

In order to create the reconstructed space for the

time series x(t

), the method of delays is used (Fraser

and Swinney, 1986; Hegger et al., 1999). A set of m

vectors, called the embedding space, are formed from

time delayed values of x (t

), Equation (2). In this set,

m is the embedding dimension and τ is the time delay.

X(t

) = {x(t

),x(t

− τ),.. ., x(t

− (m − 1)τ)} (2)

When m > 2D + 1, where D is the Hausdorff dimen-

sion, the reconstructed phase space is topologically

equivalent to the original phase space (Fraser and

Swinney, 1986). The delay τ is obtained by the ﬁrst

local minimum of the mutual information function of

the signal (Fraser and Swinney, 1986).

3.3 Entropy Estimation

In order to estimate the signal entropy, an algorithm

was developed based on the one presented in (Modde-

meijer, 1989) with the optimizations shown in (Mod-

demeijer, 1999). The method is based on a simple his-

togram algorithm with bias correction and minimum

mean square error estimation. In the cited paper, the

author presents several examples that evaluate the al-

gorithm showing its reliability.

The principle of the method is to try to estimate

the probability distribution function (PDF) of the sig-

nal under study. This is performed by dividing the

function in a rectangular grid with I equally ∆x-sized

cells. The occurrences of the signal’s points in each

cell, k

, are summed. Then, the probabilities of each

cell, p

, is replaced by the estimative k

/N, where N

is the total number of samples of the signal. There-

fore, the entropy estimator of Equation (3) is ob-

tained, since the logarithms have base 2, the units are

in bits. The bias correction for this estimator for dis-

crete systems is given in Equation (4).

= −

∑



log



+ log

∆x (3)

} ≈ H

−

I − 1

(4)

An example of the use of this algorithm is now

shown. It is taken from R. Moddemeijer web-

site: http://www.cs.rug.nl/

rudy/matlab/doc/

entropy.html. A normal distributed random noise

is generated with zero mean and unity standard devi-

ation. The signal and its histogram, obtained using

30 bins, are presented in Figures 1 and 2 respectively.

The expected entropy of this signal is 1.4189 nat. Us-

ing the estimator the result is 1.3643, what gives an

error of 3.85%.

0 200 400 600 800 1000

−3

−2

−1

Sample

Amplitude

Figure 1: Signal of a normal distributed random noise gen-

erated with zero mean and unity standard deviation used to

illustrate the entropy algorithm.

−3 −2 −1 0 1 2 3

Amplitude

Occurrences

Figure 2: Histogram of the random noise signal used to il-

lustrate the entropy algorithm. This histogram was obtained

using 30 bins.

3.4 Analysis Method

Each voice sample was analyzed by a speech thera-

pist and had its most stationary part selected. This

stationarity was further analyzed by checking the re-

sult’s power spectrum density (PSD), verifying if only

BIOSIGNALS 2008 - International Conference on Bio-inspired Systems and Signal Processing

166

minor changes occur. This is a simple form of ob-

taining wide sense stationary (WSS) signals (Hayes,

1996).

For all the samples, this procedure resulted in at

least one second of voice sample. The result was di-

vided in parts with length of 1000 points (approxi-

mately 50 milliseconds). Each of these signals were

normalized by the absolute of its maximum value.

The PDF of these normalized signals were es-

timated according to the proposed method in order

to evaluate their entropy. Since each signal has the

same length and amplitude range, the entropy estima-

tor does not favor any of them. The analysis is per-

fomed with the mean and standard deviations values

of the signal’s entropies.

4 RESULTS

Healthy and nodule voice samples analyzed by means

of phase space reconstruction technique with ANL

showed different visual patterns for each group.

In order to determinate the visual pattern charac-

teristics, three kind of orbits’ dynamic behavior were

observed: a) number of loops, b) attractor course reg-

ularity, and c) attractor trajectories distribution (di-

vergence and convergence of attractor orbits’ trajec-

tories).

For healthy voice signals, phase space reconstruc-

tion for sustained vowel /a/ presents a typical visual

pattern. First, it is characterized by many concentric

loops of different dimensions. The orbits’ loops are

correlated to the interaction between the fundamen-

tal frequency (F

) and the harmonic frequencies (F

, F

, ...) of the signal. This conﬁguration links the

voice signal complexity and the number of harmonic

frequencies ampliﬁed and contained in sustained /a/

vowel. Second, the attractor course is ﬂat and regular

and, third, the attractor trajectories are very close to

each other showing convergence tendency.

Figure 3 shows a typical healthy voice signal of a

sustained vowel /a/. Figure 4 shows its phase space

reconstruction with time delay τ according to (Fraser

and Swinney, 1986).

For nodule voice signals, phase space reconstruc-

tion of sustained vowel /a/ presents different patterns.

In general, the nodule’s pattern is characterized ﬁrstly

by a single and irregular orbit loop differing from the

healthy ones. Although the harmonic components are

present in the glottal pulse, the higher muscle tension

and subglottal pressure unbalance the (F

)/harmonic

frequencies ratio and the compensatory vocal tract

gesture contributes to atenuate the harmonic frequen-

cies, consequently producing a single trajectory loop.

0 10 20 30 40 50

−1

−0.8

−0.6

−0.4

−0.2

0.2

0.4

0.6

0.8

Time [ms]

Normalized Amplitude

Figure 3: Example of a typical healthy voice signal of a

sustained vowel /a/.

−1 −0.5 0 0.5 1 1.5

−0.75

−0.5

−0.25

0.25

0.5

0.75

x[n]

x[n−τ]

Figure 4: Phase space reconstruction of the typical healthy

voice signal of a sustained vowel /a/.

Secondly, the attractor course is irregular and curly

because of the incomplete closure of the vocal folds,

turbulence of airﬂow and the asymmetrical vibration.

Thirdly, the attractor trajectories present a disperse

tendency caused by air ﬂow volume changes and the

mucosal wave variation. This irregularity can happen

in some speciﬁc regions or even in different regions

of the orbits.

Figure 5 shows a typical nodule voice signal of a

sustained vowel /a/. Figure 6 shows its phase space

reconstruction with time delay τ according to (Fraser

and Swinney, 1986).

After the proper stationary regions of the signals

were selected using the perceptual acoustic analysis

and study of the phase space, the entropy estimations

were performed. Since these selected samples had at

least one second of voice, they were decomposed in

20 signals of 1000 points each. Figure 7 presents the

mean and standard deviation entropy values of the re-

sults of these 20 signals for each of the 14 healthy and

14 nodule voice samples. These samples are ordered

by their evaluation, therefore they are not paired.

As can be seen in the ﬁgure, the mean values of

VOICE SIGNALS CHARACTERIZATION THROUGH ENTROPY MEASURES

167

1 2 3 4 5 6 7 8 9 10 11 12 13 14

5.4

5.5

5.6

5.7

5.8

5.9

6.1

6.2

6.3

Sample

Entropy [bits]

Healthy Samples

Nodule Samples

Figure 7: Entropy estimation results for the two groups of voice signals, healthy and nodule affected, each with 14 samples.

Every point is a mean (with standard deviation) of entropy values of 20 signals (50 milliseconds each). The nodule group

presented higher values than the healthy group, 99.75% probability in a Student-t test (signiﬁcance level of 5%).

0 10 20 30 40 50

−1

−0.8

−0.6

−0.4

−0.2

0.2

0.4

0.6

0.8

Time [ms]

Normalized Amplitude

Figure 5: Example of a typical nodule voice signal of a sus-

tained vowel /a/.

−1 −0.5 0 0.5 1 1.5

−0.75

−0.5

−0.25

0.25

0.5

0.75

x[n]

x[n−τ]

Figure 6: Phase space reconstruction of the typical nodule

voice signal of a sustained vowel /a/.

the nodule samples seem to be higher than that of

the healthy samples. According to the standard de-

viation values, the two classes seem to be separated.

The mean entropy value of the healthy group is 5.76

bits with standard error of 0.14 bits, while the mean

and standard error values of the nodule group is 6.04

and 0.16 respectively. The individual values obtained

for these samples are shown in Table 1. An unpaired

Student-t test with a signiﬁcance level of 5% was per-

formed on the data. It shows that the mean of the

nodule group is indeed higher than that of the healthy

group with a probability of 99.75%.

Table 1: Mean and standard deviation (Std) of the entropy

values, in bits, of the results of the 20 signals of each of the

14 healthy and 14 nodule voice samples.

Healthy Samples Nodule Samples

Mean Std Mean Std

5.48 0.13 5.65 0.06

5.81 0.05 6.06 0.04

5.74 0.06 6.26 0.05

5.91 0.13 5.97 0.06

5.61 0.06 6.07 0.09

5.58 0.11 6.16 0.05

5.69 0.08 6.16 0.12

5.93 0.06 6.08 0.12

5.89 0.09 6.02 0.09

5.66 0.04 5.89 0.13

5.85 0.11 6.26 0.05

5.85 0.07 5.91 0.12

5.93 0.06 5.93 0.08

5.75 0.08 6.15 0.09

BIOSIGNALS 2008 - International Conference on Bio-inspired Systems and Signal Processing

168

Table 2: Mean values and standard deviations of jitter,

shimmer and pitch amplitude (PA) for the signals under

analysis (percentual values).

Samples Jitter Shimmer PA

Healthy 0.47 ± 0.39 3.34 ± 0.88 54 ± 12

Nodule 3.37 ± 3.22 10.04 ± 4.74 36 ± 15

In order to compare the performance of the proposed

method, the voice signals were analyzed aiming to

extract vocal acoustic parameters. This was per-

formed by a commercial software called An

alise de

Voz (Voice Analysis) version 6.0. The mean values

(and standard deviations) of jitter, shimmer and pitch

amplitude (PA) over the 14 samples of each group of

signals are presented in Table 2.

The jitter and shimmer mean values are smaller

for the healthy group, as expected, and present nar-

row probability distribution. For the nodule group the

distribution is much wider. This variation can be in-

terpreted as an increase of the uncertainty of these sig-

nals. The mean PA is higher for the healthy group

because the signals have a more deﬁned period, the

cause of the smaller jitter values.

The higher variability of the parameters for the

nodule group is probably due to physiological differ-

ences among the occurences of the pathology. Nod-

ules can be manifested in several ways along the vo-

cal folds, some layers of tissue may be modiﬁed or

not. Therefore, the system dynamic alterations can

lead to much different voice signals. It is interesting

to observe that the presented parameters compare fa-

vorably to the results obtained by the entropy method.

5 CONCLUSIONS

In this work, there was an attempt to look into voice

as a dynamical signal and, consequently, explore new

processing techniques for healthy and vocal nodule’s

voice signals. A practical application and advantages

of dynamical analysis were also presented. Thus,

we believe that nonlinear dynamics tools, as entropy

measures and phase space reconstruction, may help in

a review of many of the voice dynamic characteristics.

We presented a study of the use of entropy mea-

sures to two groups of voice signals. They were com-

posed by samples of healthy and nodule in the vo-

cal folds affected individuals. The samples were an-

alyzed by a speech therapist with aid of phase space

plots. The most stationary parts of these signals (in

the WSS sense) were selected. The entropy method

developed by (Moddemeijer, 1989) was used to es-

timate the entropy of samples of 50 milliseconds of

each of the signals. The results obtained for the

mean and standard deviation values were tested with

a Student-t test being clearly separable. This is an

indication of the behavior of the entropy of nodule

signals, at least in the voice samples studied.

The nodule group showed a higher entropy value

than the healthy group. This was expected because

this vocal fold pathology is characterized by increase

of the signal’s complexity (Hammarberg, 1998; Hill-

man et al., 1990). This effect is reﬂected in an in-

crease of the uncertainty of the signal, that is, the sig-

nal becomes less predictable (Crutchﬁeld and Feld-

man, 2003; Schneider and Grifﬁes, 1999).

The results were compared to jitter, shimmer and

pitch amplitude values of the samples, which were ob-

tained with a commercial software. The variability of

the parameters for the nodule affected group was sig-

niﬁcantly higher than that of the healthy group, there-

fore presenting a behavior that compares favorably to

that obtained with the entropy method.

This work is still an initial study, but phase space

analysis helps to depict the vowel pattern in a dynam-

ical way. This technique allows to visualize the dif-

ferential dynamics between healthy voices and voices

with vocal folds nodules. Future works intend to use

predictability measures to improve the understanding

of the relation of pathologies with the complexity of

the voice signal. Also, measures applied directly to

the phase space of the signals are planned as well.

ACKNOWLEDGEMENTS

The authors acknowledge the Research Foundation of

the State of S

ao Paulo (FAPESP) and the Program of

Students - Post-graduation Agreement (PEC-PG) for

the support and scholarship. We also thank the School

of Engineering of S

ao Carlos (EESC/USP) for the re-

search facilities and the use of its voice database.

REFERENCES

Amig

o, J. M., Kocarev, L., and Tomovski, I. (2007). Dis-

crete entropy. Physica D: Nonlinear Phenomena,

228(1):77–85.

Colton, R. H. and Casper, J. K. (1996). Understanding voice

problems: a physiological perspective for diagnosis

and treatment. Williams & Wilkins, Baltimore.

Cover, T. M. and Thomas, J. A. (1991). Elements of Infor-

mation Theory. John Wiley and Sons, Inc., New York.

Crutchﬁeld, J. P. and Feldman, D. P. (2003). Regularities

unseen, randomness observed: levels of entropy con-

vergence. Chaos, 13(1):25–54.

VOICE SIGNALS CHARACTERIZATION THROUGH ENTROPY MEASURES

169

Dajer, M. E., Pereira, J. C., and Maciel, C. D. (2005). Non-

linear dynamical analysis of normal voices. In Seventh

IEEE International Symposium on Multimedia (ISM

2005), pages 765–771, Irvine, CA, USA.

Davis, S. B. (1979). Speech and language: advances in

basic research and practice, chapter Acoustic char-

acteristics of normal and pathological voices, pages

271–314. Academic Publishers, New York.

Fisher, K. V. (1996). Vocal fold nodules. Curr. Op. Otol.

Head Neck Surg., 4:166–171.

Fraser, A. M. and Swinney, H. L. (1986). Independent coor-

dinates for strange attractors from mutual information.

Phys. Rev. Lett., 33(2):1134–1140.

Hammarberg, B. (1998). Perception and acoustics of voice

disorders: a combined approach. In Proceedings of

VOICEDATA98, Symposium on databases in voice

quality research and education, pages 1–6, Utrecht,

The Netherlands. Utrecht Institute of Linguistics.

Hayes, M. H. (1996). Statistical Digital Signal Processing

and Modeling. John Wiley & Sons, Inc., New York.

Hegger, R., Kantz, H., and Schreiber, T. (1999). Practical

implementation of nonlinear time series methods: The

tisean package. Chaos, 9(2):413–435.

Hillman, R. E., Holmberg, E. B., Perkell, J. S., Walsh, M.,

and Vaughan, C. (1990). Phonatory function associ-

ated with hyperfunctionally related vocal fold lesions.

Journal of Voice, 4(1):52–63.

Hirano, M. (1991). Phonosurgery assessment and surgical

management of voice disorders, chapter Phonosurgi-

cal anatomy of the larynx, pages 34–36. Raven Press,

New York.

Hugh-Munier, C. M., Scherer, K. R., Lehmann, W., and

Scherer, U. (1997). Coping strategies, personality, and

voice quality in patients with vocal fold nodules and

polyps. Journal of Voice, 11(4):452–461.

Jiang, J. J. and Titze, I. R. (1994). Measurements of vo-

cal fold pressure and impact stress. Journal of Voice,

8(2):132–145.

Kantz, H. and Schreiber, T. (2004). Nonlinear Time Series

Analysis. Cambridge University Press, Cambridge,

2nd edition.

Kirk, S. R. and Jenkins, S. (2004). Information theory-

based software metrics and obfuscation. The Journal

of Systems and Software, 72(2):179–186.

Kleeman, R. (2002). Measuring dynamical prediction util-

ity using relative entropy. Journal of the Atmospheric

Sciences, 59(13):2057–2072.

Kumar, A. and Mullick, S. K. (1996). Nonlinear dynamical

analysis of speech. Journal of the Acoustic Society of

America, 100(1):615–629.

Lake, D. E., Richman, J. S., Grifﬁn, M. P., and Moorman,

J. R. (2002). Sample entropy analysis of neonatal

heart rate variability. Am. J. Physiol. Regul. Integr.

Comp. Physiol., 283(3):R789–R797.

Moddemeijer, R. (1989). On estimation of entropy and mu-

tual information of continuous distributions. Signal

Processing, 16(3):233–248.

Moddemeijer, R. (1999). An efﬁcient algorithm for select-

ing optimal conﬁgurations of ar-coefﬁcients. In 20th

Symp. on Information Theory in the Benelux, pages

189–196, Haasrode (B).

Ott, E., Sauer, T., and Yorke, J. A. (1994). Coping with

Chaos. John Wiley & Sons, Inc., New York.

Packard, N. H., Crutchﬁeld, J. P., Farmer, J. D., and Shaw,

R. S. (1980). Geometry from a time series. Phys. Rev.

Lett., 45(9):712–716.

Rabiner, L. R. and Schafer, R. W. (1978). Digital Pro-

cessing of Speech Signals. Prentice Hall, Englewood

Cliffs, NJ.

Rosa, M. O., Pereira, J. C., and Grellet, M. (2000). Adap-

tive estimation of residue signal for voice pathology

diagnosis. IEEE Trans. Bio. Eng., 47(1):96–104.

Rosen, C. A. and Murry, T. (2000). Nomenclature of voice

disorders and vocal pathology. Otolaryngol. Clin.

North. Am., 33(5):1035–1046.

Scalassara, P. R., Maciel, C. D., Guido, R. C., Pereira,

J. C., Fonseca, E. S., Montagnoli, A. N., Barbon, S.,

Vieira, L. S., and Sanchez, F. L. (2007). Autoregres-

sive decomposition and pole tracking applied to vo-

cal fold nodule signals. Pattern Recognition Letters,

28(11):1360–1367.

Schneider, T. and Grifﬁes, S. M. (1999). A conceptual

framework for predictability studies. Journal of Cli-

mate, 12(10):3133–3155.

Shannon, C. E. (1948). A mathematical theory of commu-

nication. The Bell System Technical Jounal, 27:379–

423, 623–656.

Titze, I. R. (1994). Mechanical stress in phonation. Journal

of Voice, 8(2):99–105.

Uloza, V., Saferis, V., and Uloziene, I. (2005). Perceptual

and acoustic assessment of voice pathology and the ef-

ﬁcacy of endolaryngeal phonomicrosurgery. Journal

of Voice, 19(1):138–145.

BIOSIGNALS 2008 - International Conference on Bio-inspired Systems and Signal Processing

170