Classification of Peterson & Barney's vowels using Weka
Aldebaro Klautau
UC San Diego - EBU - I
La Jolla, CA 92093-0407
Email: a.klautau@ieee.org
February 29, 2002
1. Introduction
Gordon Peterson and Harold Barney describe a detailed investigation of sustained
American English vowels in [1]. The article presents acoustic measurements of fundamental
frequency (F0) and first three formant frequencies (F1-F3). The authors also conducted
experiments where listeners were asked to identify words.
Raymond Watrous [2] re-organized the database collected in [1] and made it temporarily
available from University of Pennsylvania. In 1994, Murray Spiegel posted a message on
comp.speech news group1 indicating the database had been made available again, but from
Bellcore. Later, Tony Robinson made it permanently available from Cambridge University2. Now
the database, formatted for Weka [3], is also available from [4]. It is called the pbvowel database
because Robison has made available another database that is usually identified as vowel in [5].
The vowel database consists of eleven sustained vowels of British English collected by
David Deterding and represented by log-area ratio (LAR) parameters. When using the standard
partitions into test and train sets3, the error rates for the vowel database are usually higher (around
twice) than for pbvowel. Besides being based on different English accents, the vowel and pbvowel
databases were not obtained through the same experimental procedures. Also, formants can be
seen as a more efficient representation of vowels than LAR parameters. LAR is a well-known,
but outdated parameterization of speech [6]. In speech coding the LARs were substituted by the
line spectral frequencies [7] and in speech recognition, parameters obtained through cepstrum
analysis are more popular [8].
The motivations for writing this report about pbvowel were:
- it has been used by several researchers (e.g. [9], [10], [11]) but their results can not be easily
compared due to the lack of a standard experimental procedure;
- the open-source Weka machine learning package [3] provides implementations of several
classical pattern recognition techniques. The command lines for Weka are provided here, so
the reported results can be easily reproduced;
- the conventional nomenclature for formants (F1, F2 and F3) and fundamental frequency (F0)
is confusing. Some publications mistakenly mention that pbvowel contains four formants (e.g.
[11], [2]). It seems important to present their definitions and emphasize the distinction
between F0 and formants;
- [1] completes 50 years in 2002 and deserves a celebration!

1
This group was later split in comp.speech.users and comp.speech.research.
2
The file is called PetersonBarney.tar.Z and is available at ftp://svr-ftp.eng.cam.ac.uk/pub/comp.speech/data/.
3
The error rate when using n-fold cross-validation is usually considerably smaller.
This report is organized as follows. Section 2 presents a brief description of the concepts
of formants and fundamental frequency, the numerical attributes of the pbvowel database. Section
3 reviews the work reported in [1]. A partition of the database is presented in section 4. The
results of vowel classification using Weka are reported in section 5. Section 6 shows some plots
obtained considering only the first two formants. The final considerations are in section 7.
2. Speech formants and fundamental frequency
In the Fifties, Gunnar Fant made significant contributions to the development of an
acoustic theory of speech where the speech wave is seen as the response of the vocal tract filter
systems to one or more sound sources. This is the basic principle of the so-called source-filter
model of the speech production process. A detailed description of this model can be found in
[12]. Given the scope of pbvowel, it suffices to consider here only the production of vowels.
Fundamental frequency (F0):
When a vowel is produced, the vocal cords vibrate on a rate called fundamental frequency
or F0. In practice, F0 is not exactly the same over time but varies intentionally or unintentionally
(machines can produce a monotonic F0 though). The average F0 values of children are higher
than of adults, and women have higher F0 than men, as can be inferred from pbvowel. F0 is a
parameter related to the source (as discussed later, the formants are related to the filter).
The pitch frequency is closely related to F0 and in many cases these terms are used
interchangeably. In more strict terminology, pitch is a tonal sensation and frequency a property of
the sound stimulus [12]. It is not an easy task to estimate F0, but it is harder to quantify the
subjective sensation of pitch. The mel scale [13], which is popular in speech recognition, is an
attempt to relate frequency and pitch.
The method used for estimating F0 in [1] is not discussed by the authors (neither in the
companion paper [14]).
Formants:
The main articulators involved in vowel production are tongue and lips. Depending on
their configuration the vocal tract imposes different shapes to the resultant speech spectrum. The
source-filter model assumes the source spectrum S(f) is modified by the filter (vocal tract)
function T(f), leading to a speech spectrum P(f) = S(f) T(f). For vowels, S(f) is basically composed
by harmonics of F0. The speech formants can be defined either as the peaks of |S(f)| or |T(f)|,
which generates some confusion. From [12] (page 20):
"The spectral peaks of the sound spectrum |P(f)| are called formants. (…) it may be seen that one
such resonance has its counterpart in a frequency region of relatively effective transmission
through the vocal tract. This selective property of |T(f)| is independent of the source. The
frequency location of a maximum in |T(f)|, i.e., the resonance frequency, is very close to the
corresponding maximum in spectrum P(f) of the complete sound. Conceptually these should be
held apart but in most instances resonance frequency and formant frequency may be used
synonymously. Thus, for technical applications dealing with voiced sounds it is profitable to
define formant frequency as a property of T(f)."
Modern textbooks4 define formants as the resonance frequencies associated to T(f) [16]
(page 18), [8] (page 27). As pointed out by Fant, this definition is sensible because eliminates the
influence of the source characteristics, which are speaker-dependent (e.g. different people say the
same vowel with potentially different values of F0). On the other hand, it raises the problem that
resonances of T(f) are sometimes undetermined given that usually only a measure of P(f) is
available. For example, a person (e.g. child) with high F0 would produce S(f) with harmonics of
F0 highly separated in frequency, so the peaks of T(f) would be hardly visualized if they were far
from any harmonic.
There are many techniques for estimating formants. A survey of formant estimation
methods used in the past is given in [17] (page 165). A popular modern approach is to obtain
formants from the roots of a filter calculated through linear prediction techniques [6]. Fig. 1 and
Fig. 2 show spectrograms [6] with formant tracks (F1-F3) superimposed. The first sentence is
composed basically by vowels and the method gives fairly good results. The sentence
correspondent to Figure 2 has more phonetic variation (fricatives, nasals, etc.) and the results are
not so good as in Figure 1. In fact, under realistic conditions (noise, etc.), formants estimation is a
difficult task.
Time (sec)
Fr
eq
ue
nc
y
(H
z)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
500
1000
1500
2000
2500
3000
3500
4000
Fig. 1. First three formants F1- F3 estimated from the roots of linear prediction filters of order 8. The
sentence is "We were away" spoken by a male speaker with low F0.

4
Kenneth Stevens observes that the concept of a formant should be restricted to natural frequencies of the vocal tract
when there is no coupling to the nasal cavities [15] (page 131).
Fig. 2. First three formants F1-F3 estimated from the roots of linear prediction filters of order 8. The sentence
is "In wage negotiations, the industry bargains as a unit with a single union".
The method for estimating formants used in [1] is described, though not thoroughly, in
[14]. It consists of calculating a weighted average of the spectrum components. This approach is
known as "peak-picking" and, as other formant estimation methods, is error prone and usually
requires the supervision of an expert for eventual corrections.
3. Peterson & Barney's paper
Data collection
A list of ten words was presented to 76 speakers, each word beginning with [h] and
ending with [d], and differing only in the vowel. The words are listed in Table I. Each speaker
was asked to pronounce two different lists, each list corresponding to a random permutation of
the 10 words. Therefore, the total number of recorded words was 1520.
The first formant F1 can be related to how far the tongue is raised and F2 to which part of
the tongue is raised. Therefore, vowels can be organized according to the tongue's position in
plots as Fig. 3. Nowadays phoneticians point out that pictorial representations as Fig. 3 should be
seen as first-order approximations, given that it is actually possible to produce a vowel with a
configuration radically different from the one suggested by Fig. 3 [18].
Fig. 3. Relations between formants and tongue's positions. Note that the F1 and F2 axes should have the
directions indicated by Figure 2 in order to provide the picture popular among phoneticians.
The vowels are identified in Fig. 3 by symbols defined in the International Phonetic
Alphabet (IPA). The IPA makes extensive use of letters not available on computers. The
ARPABET is one of the proposed mappings from IPA to ASCII symbols. The vowels in pbvowel
were labeled according to the two-characters representation of the ARPABET5. Table I shows the
words and correspondent vowels. More details about these phonetic symbols can be found in [18]
(page 29).
Table I - Words used in [1] and the correspondent vowels. The actual sounds can be heard at [20]. The IPA
diacritic indicates the vowel has longer duration and the "hook" diacritic

indicates the vowel

is
influenced ("colored") by [r].
Word used
in [1]
IPA
symbol for
the vowel
More
detailed IPA
transcription
ARPABET
symbol
Example in
context /h_/
Example in
context
/b_d/
Example in
context
/h_t/
Example in
context
/k_d/
heed

IY he bead heat keyed
hid

IH
−
bid hit kid
head

EH
−
bed
− −
had

AE
−
bad hat cad
hod


AA
−
bod hot cod
hawed



AO haw bawd
−
cawed
hood

UH
− − −
could
who'd

UW who booed hoot cooed
hud

AH
−
bud hut cud
heard


ER her bird hurt curd

5
An on-line version of the ARPABET can be found at [19].
Listening tests
The 1,520 recorded words were presented to a group of 70 adult observers. Thirty-two of
the 76 speakers were also among the observers. The experiment was conducted in seven sessions.
The general purpose of these tests was to obtain an aural classification of each vowel. Each
observer would mark the word he heard. For each vowel, all correspondent 152 words were
presented to the observers. The ease with which the observers classified the various vowels
varied significantly. Of all IY sounds, for instance, 143 were unanimously classified by all
observers as IY. On the other hand, only 9 when the intended vowel was AA. This result is
summarized in Fig. 4. From [1]: "The very low scores of AA and AO result primarily from the fact
that some members of the speaking group and many members of the listening group speak one of
the forms of American dialects in which AA and AO are not differentiated."
% recognized unanimously by 70 listeners
94.08
48.68
34.21
75.66
5.92
22.37
50.00
71.71
50.00
90.79
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
100.00
IY IH EH AE AA AO UH UW AH ER
Fig. 4. The percentage unanimously identified by all 70 listeners of 152 repetitions for each vowel.
The complete confusion matrix is shown in Table II. A graphical representation of the
confusion matrix is shown in Fig. 5. The total average "error" of the listening test was 5.57 %.
Table II - Confusion matrix for listening experiment in [1]. Lines indicate the intended, and columns the vowel
understood by listeners. The last two columns show the total6 and error per line.
IY IH EH AE AA AO UH UW AH ER Total %
error
IY 10267 4 6
− −
3
− − − −
10280 0.13
IH 6 9549 694 2 1 1
− − −
26 10279 7.10
EH
−
257 9014 949 1 3
− −
2 51 10277 12.29
AE
−
1 300 9919 2 2
− −
15 39 10278 3.49
AA
−
1
−
19 8936 1013 69
−
228 7 10273 13.01
AO
− −
1 2 590 9534 71 5 62 14 10279 7.25
UH
− −
1 1 16 51 9924 96 171 19 10279 3.45
UW
− −
1
−
2
−
78 10196
−
2 10279 0.81
AH
−
1 1 8 540 127 103
−
9476 21 10277 7.79
ER
− −
23 6 2 3
− −
2 10243 10279 0.35

6
Each vowel should be voted 10640 (152 × 70) times, but the "Total" column shows the actual average number is
around 10279. The total number of votes was 102780, indicating that 3620 from the expected total of 106400 votes
were not considered when organizing the table. The reasons for that are not mentioned in [1].
Some instances in pbvowel are labeled as being unanimously classified by all observers. It
should be noticed that the documentation available with the pbvowel version distributed by
Cambridge University mentions only 26 observers, while 70 were reported in [1]. In fact, the
statistics of the vowels in pbvowel that were labeled as unanimously classified does not match the
results in [1]. In pbvowel, only 321 vowels were labeled as not unanimously identified by
observers. The reason for this discrepancy on the number of observers is unknown.
Fig. 5. Graphical representation of the confusion matrix for the listening test in [1]. The columns indicate the
recognized vowel. The radii are proportional to the entries in Table II. The last column illustrates the
difficulty on recognizing each vowel.
Acoustic measurements
Besides F0 and three formants, the formant amplitudes in dB were also reported in [1],
but are missing in pbvowel. The statistics for F0 and formants F1-F3 are listed in Table III.
Table III- Statistics of the numerical attributes in pbvowel: minimum, maximum, average and standard
deviation for all 1,520 instances.
Min Max Average Std
F0 91 350 191.29 60.36
F1 190 1300 563.30 201.25
F2 560 3610 1624.38 637.01
F3 1400 4380 2707.81 519.45
4. Partitioning the database
The attributes for the version of pbvowel distributed by [5] are listed in Table IV. In
classification experiments, the attributes speaker_number and confidence should not be used.
A partition of pbvowel into four subsets based on the speaker identity is presented in this
section. All subsets have 19 speakers, corresponding approximately to the same number of males,
females and children. An open test set framework is adopted, i.e., speakers in the train do not
belong to the test set. The standard partition is a train set corresponding to the union of A and B
(with C and D corresponding to the test set). Eventually, if a given algorithm demands more
training data, set C can be used for training and the situation properly reported. Alternatively, set
C can be used as a validation set.
Table IV- Attributes of pbvowel.
Attribute name Type
gender_age nominal: {male, female, child}
speaker_number numerical, integer ∈ [1, 76]
confidence nominal: {low, high}
F0 numerical, integer
F1 numerical, integer
F2 numerical, integer
F3 numerical, integer
vowel nominal: {IY,IH,EH,AE,AA,AO,UH,UW,AH,ER}
Table V- Partition of pbvowel into four disjoint subsets according to speaker identity. All sets have 380 vowels,
corresponding to 19 speakers.
Set Males Females Children
A 1-8 34-40 62-65
B 9-16 41-47 66-69
C 17-24 48-54 70-73
D 25-33 55-61 74-76
It may be interesting to consider only the instances that were labeled as unanimously
identified by the listeners, i.e., those with attribute confidence equal to high. A suffix "u", as
shown in Table VI, identifies the corresponding subsets. The training set composed by A_u and
B_u contains 599 instances, while the test set (C_u and D_u) contains 600. The distribution of
vowels is not uniform when considering only the ones unanimously identified.
Table VI- Number of vowels unanimously identified by listeners in each set in Table V.
Set A_u B_u C_u D_u
# of vowels 289 310 295 305
Table VII- Identifiers for simulations using different combinations of the attributes in pbvowel.
Identifier Used attributes (besides the vowel)
gF0-3 gender_age, F0, F1, F2, F3
F0-3 F0, F1, F2, F3
F1-3 F1, F2, F3
F1-2 F1, F2
u (as prefix, e.g., uF0-F3) only instances with confidence equal to high
This report presents simulations with different combinations of the attributes in pbvowel.
Table VII summarizes these combinations. For example, a simulation identified by uF1-3 uses a
train set composed by instances for which confidence is high, and discarding attributes
gender_age, speaker_number, confidence and F0.
5. Classification using Weka
This section presents results obtained with Weka, version 3.2. Weka can be obtained at
[3] and the source code in Java is also available. Table VIII shows results obtained with 20
different classifiers, for 5 different combinations of attributes as described in Table VII. The
command lines for reproducing these results are given in the Appendix. The best results in Table
VIII are also the best in the literature that the author is aware of. However, some classifiers were
not tuned, as Table VIII was designed to serve simply as basis for comparisons. For example, the
default in Weka's multilayer perceptron is a number of units in the hidden layer given by the
average between the number of attributes and classes (e.g., (4+10)/2 = 7 units for the first column
F0-3). Tuning the network topology leads to improvements. However, it is questionable to use
the test set to validate parameters, i.e., choosing the parameters that lead to the best results for the
test set, implies the performance on this set does not necessarily indicate the generalization
capability of the classifier. A better approach in this case would be to use set C as a validation set
and report results on set D. Here, the default values were used for most classifiers and a
validation set was not adopted.
It can be seen from Table VIII that the extra attribute gender_age in ugF0-3 does not
bring better results when compared to uF0-3. In fact, as discussed in section 2, F0 alone does not
bring information about vowel identity. However, F0 is related to attribute gender_age. Given
that vowels (and consequently F1-F3) vary depending if the speaker is a man, woman or child,
F0 or gender_age can improve classification accuracy if the classifier effectively uses this
information. For classifiers as Naïve Bayes, which assumes independence among attributes given
the class, F0 and gender_age do not help.
For an easier visualization, the results of Table VIII are also shown in Fig. 6. The reader is
refereed to the Weka documentation for an explanation of acronyms as ECOC (error-correcting
output code), etc.
Table VIII - Misclassification rate for 20 classifiers designed with Weka. The columns are labeled according to
Table VII. The best result for each data set is indicated in bold.
# Algorithm and configuration F0-3 ugF0-3 uF0-3 uF1-3 uF1-2
1 Naïve Bayes - simpler implementation 24.74 21.33 21.00 21.33 26.83
2 Naïve Bayes 24.60 21.17 21.50 22.00 27.17
3 Naïve Bayes with kernel estimation 22.10 19.00 17.83 19.50 25.00
4 Kernel density estimator 17.37 13.50 13.17 13.33 18.67
5 K-nearest neighbor with K = 5 16.58 13.50 13.17 14.33 21.50
6 K-nearest neighbor with entropic distance (KStar) 16.84 11.83 12.33 12.67 18.33
7 Multilayer perceptron 13.42 12.83 9.83 15.50 19.67
8 C4.5 decision tree with reduced error pruning 23.29 20.5 21.5 19.83 27.83
9 Bagging 10 iterations using C4.5 with reduced error
pruning
19.08 14.67 14.33 16.00 20.33
10 Bagging 50 iterations using C4.5 with reduced error
pruning
17.89 14.33 14.67 17.83 22.00
11 AdaBoost M1 using C4.5 without reduced error
pruning
16.05 14.33 14.00 16.17 29.50
12 AdaBoost M1 using C4.5 with reduced error pruning 18.29 17.50 16.83 19.17 26.83
13 Boosted stumps with LogitBoost 20.00 18.33 18.50 19.50 24.17
14 10 binary classifiers (one-against-all): SVM with
polynomial kernel of order 5
15.92 11.17 11.50 17.17 28.83
15 10 binary classifiers (one-against-all): 50 iterations of
AdaBoost using stumps
19.34 16.50 17.83 19.50 27.83
16 10 binary classifiers (one-against-all): 50 iterations of
LogitBoost using stumps
19.60 15.83 15.67 18.67 23.50
17 10 binary classifiers (one-against-all): multilayer
perceptron
12.89 10.50 10.33 11.00 21.17
18 20 binary classifiers (random code): multilayer
perceptron
14.60 11.33 9.83 22.83 30.83
19 20 binary classifiers (random code): 100 iterations of
AdaBoost using stumps
31.58 22.50 22.33 27.83 30.00
20 20 binary classifiers (random code): 10 iterations of
AdaBoost using multilayer perceptrons
12.63 10.00 10.00 11.67 22.33
0 5 10 15 20 25 30 35
1- Naïve Bayes
2- Naïve Bayes
3- Naïve Bayes
4- Kernel estimator
5- KNN
6- KNN
7- ANN
8- C4.5
9- Bagged 10 C4.5
10- Bagged 50 C4.5
11- Boosted C4.5
12- Boosted C4.5
13- LogitBoosted stumps
14- SVM
15- ECOC boosted stumps
16- ECOC boosted stumps
17- ECOC ANN
18- ECOC ANN
19- ECOC boosted stumps
20- ECOC boosted ANN
uF1-2
uF1-3
uF0-3
ugF0-3
F0-3
Fig. 6. Illustration of misclassification rates shown in Table VIII.
Fig. 7 compares the results obtained with the neural network classifier correspondent to
number 17 in Table VIII with the listening experiments in [1]. The pattern of errors is not exactly
the same, but there are coincidences as, for example, vowels IY and ER are recognized with high
accuracy in both cases. In relative terms, the machine has more troubles with UH, while listeners
have with AA.

Fig. 7- Confusion matrices for listening test (Fig. 5) at the left and results with neural network (number 17 in
Table VIII) at the right. The columns indicate the recognized vowel. The radii are proportional to the entries.
6. Visualization of results on F1 x F2 plane
As shown in this section, illustrative plots can be obtained when using only the first two
formants. The figures in this section use color for an easier visualization.
Fig. 8 shows the instances used for training and testing the classifiers discussed in this
section (see the appendix for other plots) Note that the regions overlap significantly in the F1 x
F2 plane, especially for vowel ER. In spite of being perceptually less important than F1 and F2,
the third formant F3 is useful for distinguishing ER from the others. In fact, according to Table II,
ER can be easily recognized by listeners.
Fig. 8. Plot of all instances for which confidence is high (identified unanimously).
iy
iy
ihih
eh
ae
ahah
aa aauhuhuw
uw
er
er
iy
iy
ihih
eh
ae
ae
aaaa
aoao
uh
uh
uwuw
er
er
iy
iy
ihih
eheh ae
ah
aa a
aoao
uh
uh
uw
erer
iy
iy
ih
eh
eh
aeae
ah
aa aa
uhuhuw
uw
erer
iyiy
ih eh
eh aeae
ah
ah aa
ao
uhuh
uw
erer
iyiy
ihi
eheh
ae ae
ah
uhuh
uw
uw
err
iyiy
ih
eh aeae
ah
aa
ao
ao
uw
er
er
iy
ih
ahah
ao
uh
uh
uw
erer
iyiy
ihi
eh
ehae
ah aa
aoao
uh
uw
uw
er
r
iiy
ihih
eh
ae
ahah
aa
ao
erer
iyiy
i ih
ae
ah
ao
uhuh
uw
er
er
iyiy
ihih
eheh ae
auhuh
uw
uw
erer
iy
ihih
eh
eh
ae ae
ah ah aa
ao
uhuhuw
r
er
iyiy
ih
i
eheh
aeae
ah
ah
aa
aa
ao
uh
uw
uw
erer
iy
ih
aeae
ah
aaaa
aoao
uhuh
uw
er
er
iyiy
ihih
aeae
ao
uh
uwuw
erer
iyiy
ih
ih
eh
eh
ae
ae
ah
ao
uh
uwuw
er
iyiy
ih
ih
eh
eh
ae
ahah
aa
ao
uh
uh
w
uw
er
er
iy
ihih eh
ae
ah
aa
ao aouw
er
iyiy
ihih eh eh
h
aa aa
ao
uhuh
w
uw
er er
iy
iy
i eheh
ae
ae
ah
aa
aoao
uw
w
er
er
iy
iy
ih eh
eh
aeae
ah ah
aa
ao
ao
uwuw
r r
iyiy
i
ih
eh
eh
ae
ae
ah
aaa
ao
uh
uh
uw
uw
erer
iyiy
ih
i
eh
eh
ae
ah
a
aa
ao
uh
uw
uw
er
r
iy
iy
ih
ih
eh
ae
ae
ahah aa
o
uh
uw
er
r
iyiy
ih
eh
ae ae
ah
ah aa
oo
uhuh
uw
er
er
iy
iy
ae
ah
o
uh
uw
uw
er
er
iy
iy
ih
ih
eh
ae
ae
ahah
uhuh
uw
er
iy
iy
i
ah
ah
aa
aa
ao
ao
uh
uh
uw uw
er
er
iy
iy
aeae
aa
uh
uw w
er
er
iy iy
ae ae
ah
ah
aa
uh
uh
uw
erer
iy
iy
ih
eh
ae
ae
aa
o
o
uh
u
uw
uw
er
er
iy
iy
aeae
ahah
aoao
uh
uh
uw
er
er
iy
iy
ih
eh
eh ae
ae
ah
ao
uh
uh
uw
uw
er
er
F1 (Hz)
F2

(H
z
)
C4.5 decision tree. Misclassification error: 27.83%
0 200 400 600 800 1000 1200 1400
500
1000
1500
2000
2500
3000
3500
4000
Fig. 9. Decision boundaries obtained with a C4.5 decision tree (number 8 in Table VIII). The colors are the
same as in Fig. 8. The test instances are superimposed with their corresponding colors, such that errors can be
identified.
A decision tree as C4.5 leads to boundaries that are parallel to the axes as shown in Fig. 9.
This limitation is clearly problematic in this case. Some classifiers that are capable of arbitrary
decision boundaries as K-nearest neighbor and neural networks led to better results, as shown in
Fig. 10 and Fig. 11, respectively. Note that the K-nearest neighbor established a non-contiguous
region for ER.
iy
iy
ihih
eh
ae
ahah
aa aauhuhuw
uw
er
er
iy
iy
ihih
eh
ae
ae
aaaa
aoao
uh
uh
uwuw
er
er
iy
iy
ihih
eheh ae
ah
aa a
aoao
uh
uh
uw
erer
iy
iy
ih
eh
eh
aeae
ah
aa aa
uhuhuw
uw
erer
iyiy
ih eh
eh aeae
ah
ah aa
ao
uhuh
uw
erer
iyiy
ihi
eheh
ae ae
ah
uhuh
uw
uw
err
iyiy
ih
eh aeae
ah
aa
ao
ao
uw
er
er
iy
ih
ahah
ao
uh
uh
uw
erer
iyiy
ihi
eh
ehae
ah aa
aoao
uh
uw
uw
er
r
iiy
ihih
eh
ae
ahah
aa
ao
erer
iyiy
i ih
ae
ah
ao
uhuh
uw
er
er
iyiy
ihih
eheh ae
auhuh
uw
uw
erer
iy
ihih
eh
eh
ae ae
ah ah aa
ao
uhuhuw
r
er
iyiy
ih
i
eheh
aeae
ah
ah
aa
aa
ao
uh
uw
uw
erer
iy
ih
aeae
ah
aaaa
aoao
uhuh
uw
er
er
iyiy
ihih
aeae
ao
uh
uwuw
erer
iyiy
ih
ih
eh
eh
ae
ae
ah
ao
uh
uwuw
er
iyiy
ih
ih
eh
eh
ae
ahah
aa
ao
uh
uh
w
uw
er
er
iy
ihih eh
ae
ah
aa
ao aouw
er
iyiy
ihih eh eh
h
aa aa
ao
uhuh
w
uw
er er
iy
iy
i eheh
ae
ae
ah
aa
aoao
uw
w
er
er
iy
iy
ih eh
eh
aeae
ah ah
aa
ao
ao
uwuw
r r
iyiy
i
ih
eh
eh
ae
ae
ah
aaa
ao
uh
uh
uw
uw
erer
iyiy
ih
i
eh
eh
ae
ah
a
aa
ao
uh
uw
uw
er
r
iy
iy
ih
ih
eh
ae
ae
ahah aa
o
uh
uw
er
r
iyiy
ih
eh
ae ae
ah
ah aa
oo
uhuh
uw
er
er
iy
iy
ae
ah
o
uh
uw
uw
er
er
iy
iy
ih
ih
eh
ae
ae
ahah
uhuh
uw
er
iy
iy
i
ah
ah
aa
aa
ao
ao
uh
uh
uw uw
er
er
iy
iy
aeae
aa
uh
uw w
er
er
iy iy
ae ae
ah
ah
aa
uh
uh
uw
erer
iy
iy
ih
eh
ae
ae
aa
o
o
uh
u
uw
uw
er
er
iy
iy
aeae
ahah
aoao
uh
uh
uw
er
er
iy
iy
ih
eh
eh ae
ae
ah
ao
uh
uh
uw
uw
er
er
F1 (Hz)
F2

(H
z
)
KStar (-B 20 -M a). Misclassification error: 18.33%
0 200 400 600 800 1000 1200 1400
500
1000
1500
2000
2500
3000
3500
4000
Fig. 10. Decision boundaries and errors obtained with a K-nearest neighbor classifier (number 6 in Table
VIII).
iy
iy
ihih
eh
ae
ahah
aa aauhuhuw
uw
er
er
iy
iy
ihih
eh
ae
ae
aaaa
aoao
uh
uh
uwuw
er
er
iy
iy
ihih
eheh ae
ah
aa a
aoao
uh
uh
uw
erer
iy
iy
ih
eh
eh
aeae
ah
aa aa
uhuhuw
uw
erer
iyiy
ih eh
eh aeae
ah
ah aa
ao
uhuh
uw
erer
iyiy
ihi
eheh
ae ae
ah
uhuh
uw
uw
err
iyiy
ih
eh aeae
ah
aa
ao
ao
uw
er
er
iy
ih
ahah
ao
uh
uh
uw
erer
iyiy
ihi
eh
ehae
ah aa
aoao
uh
uw
uw
er
r
iiy
ihih
eh
ae
ahah
aa
ao
erer
iyiy
i ih
ae
ah
ao
uhuh
uw
er
er
iyiy
ihih
eheh ae
auhuh
uw
uw
erer
iy
ihih
eh
eh
ae ae
ah ah aa
ao
uhuhuw
r
er
iyiy
ih
i
eheh
aeae
ah
ah
aa
aa
ao
uh
uw
uw
erer
iy
ih
aeae
ah
aaaa
aoao
uhuh
uw
er
er
iyiy
ihih
aeae
ao
uh
uwuw
erer
iyiy
ih
ih
eh
eh
ae
ae
ah
ao
uh
uwuw
er
iyiy
ih
ih
eh
eh
ae
ahah
aa
ao
uh
uh
w
uw
er
er
iy
ihih eh
ae
ah
aa
ao aouw
er
iyiy
ihih eh eh
h
aa aa
ao
uhuh
w
uw
er er
iy
iy
i eheh
ae
ae
ah
aa
aoao
uw
w
er
er
iy
iy
ih eh
eh
aeae
ah ah
aa
ao
ao
uwuw
r r
iyiy
i
ih
eh
eh
ae
ae
ah
aaa
ao
uh
uh
uw
uw
erer
iyiy
ih
i
eh
eh
ae
ah
a
aa
ao
uh
uw
uw
er
r
iy
iy
ih
ih
eh
ae
ae
ahah aa
o
uh
uw
er
r
iyiy
ih
eh
ae ae
ah
ah aa
oo
uhuh
uw
er
er
iy
iy
ae
ah
o
uh
uw
uw
er
er
iy
iy
ih
ih
eh
ae
ae
ahah
uhuh
uw
er
iy
iy
i
ah
ah
aa
aa
ao
ao
uh
uh
uw uw
er
er
iy
iy
aeae
aa
uh
uw w
er
er
iy iy
ae ae
ah
ah
aa
uh
uh
uw
erer
iy
iy
ih
eh
ae
ae
aa
o
o
uh
u
uw
uw
er
er
iy
iy
aeae
ahah
aoao
uh
uh
uw
er
er
iy
iy
ih
eh
eh ae
ae
ah
ao
uh
uh
uw
uw
er
er
F1 (Hz)
F2

(H
z
)
Backpropagation neural network. Misclassification error: 19.67%
0 200 400 600 800 1000 1200 1400
500
1000
1500
2000
2500
3000
3500
4000
Fig. 11. Decision boundaries and errors obtained with a multilayer perceptron (number 7 in Table VIII).
Some classifiers, as the implementation of support vector machines (SVM) in Weka, can
not deal with more than two classes. One alternative is to break down the multiclass problem into
several binary problems. Fig. 12 shows the results obtained by training 10 binary classifiers using
a one-versus-all methodology [11].
iy
iy
ihih
eh
ae
ahah
aa aauhuhuw
uw
er
er
iy
iy
ihih
eh
ae
ae
aaaa
aoao
uh
uh
uwuw
er
er
iy
iy
ihih
eheh ae
ah
aa a
aoao
uh
uh
uw
erer
iy
iy
ih
eh
eh
aeae
ah
aa aa
uhuhuw
uw
erer
iyiy
i
ih eh
eh aeae
ah
ah aa
ao
uhuh
uw
erer
iyiy
ihi
eheh
ae ae
ah
uhuh
uw
uw
err
iyiy
ih
eh aeae
ah
aa
ao
ao
uw
er
er
iy
ih
ahah
ao
uh
uh
uw
erer
iyiy
ihi
eh
ehae
ah aa
aoao
uh
uw
uw
er
r
iy
ihih
eh
ae
ahah
aa
ao
er
er
iyiy
ih
ae
ah
ao
uhuh
uw
er
er
iyiy
ihih
eheh ae
auhuh
uw
uw
erer
iy
ihih
eh
eh
ae ae
ah ah aa
ao
uhuhuw
r
er
iyiy
ih
i
eheh
aeae
ah
ah
aa
aa
ao
uh
uw
uw
erer
iy
ih
aeae
ah
aaaa
aoao
uhuh
uw
er
er
iyiy
ihih
aeae
ao
uh
uwuw
erer
iyiy
ih
ih
eh
eh
ae
ae
ah
ao
uh
uwuw
er
iyiy
ih
ih
eh
eh
ae
ahah
aa
ao
uh
uh
w
uw
er
er
iy
ihih eh
ae
ah
aa
ao aouw
er
iyiy
ihih eh eh
h
aa aa
ao
uhuh
w
uw
er er
iy
iy
i eheh
ae
ae
ah
ah aa
aoao
uw
w
er
er
iy
iy
ih eh
eh
aeae
ah ah
aa
ao
ao
uwuw
r r
iyiy
i
ih
eh
eh
ae
ae
ah
aaa
ao
uh
uh
uw
uw
erer
iyiy
ih
i
eh
eh
ae
ah
a
aa
ao
uh
uw
uw
er
r
iy
iy
ih
ih
eh
ae
ae
ahah aa
o
uh
uw
er
r
iyiy
ih
eh
ae ae
ah
ah aa
oo
uhuh
uw
er
er
iy
iy
ae
ah
o
uh
uw
uw
er
er
iy
iy
ih
ih
eh
ae
ae
ahah
uhuh
uw
er
iy
iy
i
ah
ah
aa
aa
ao
ao
uh
uh
uw uw
er
er
iy
iy
aeae
aa
uh
uw w
er
er
iy iy
ae ae
ah
ah
aa
uh
uh
uw
erer
iy
iy
ih
eh
ae
ae
aa
o
o
uh
u
uw
uw
er
er
iy
iy
aeae
ahah
aoao
uh
uh
uw
er
er
iy
iy
ih
eh
eh ae
ae
ah
ao
uh
uh
uw
uw
er
er
F1 (Hz)
F2

(H
z)
SVM organized as 10 binary classifiers. Misclassification error: 28.83%
0 200 400 600 800 1000 1200 1400
500
1000
1500
2000
2500
3000
3500
4000
Fig. 12. Decision boundaries and errors obtained with support vector machines (number 14 in Table VIII).
iy
iy
ihih
eh
ae
ahah
aa aauhuhuw
uw
er
er
iy
iy
ihih
eh
ae
ae
aaaa
aoao
uh
uh
uwuw
er
er
iy
iy
ihih
eheh ae
ah
aa a
aoao
uh
uh
uw
erer
iy
iy
ih
eh
eh
aeae
ah
aa aa
uhuhuw
uw
erer
iyiy
i
ih eh
eh aeae
ah
ah aa
ao
uhuh
uw
erer
iyiy
ihi
eheh
ae ae
ah
uhuh
uw
uw
err
iyiy
ih
eh aeae
ah
aa
ao
ao
uw
er
er
iy
ih
ahah
ao
uh
uh
uw
erer
iyiy
ihi
eh
ehae
ah aa
aoao
uh
uw
uw
er
r
iy
ihih
eh
ae
ahah
aa
ao
er
er
iyiy
ih
ae
ah
ao
uhuh
uw
er
er
iyiy
ihih
eheh ae
auhuh
uw
uw
erer
iy
ihih
eh
eh
ae ae
ah ah aa
ao
uhuhuw
r
er
iyiy
ih
i
eheh
aeae
ah
ah
aa
aa
ao
uh
uw
uw
erer
iy
ih
aeae
ah
aaaa
aoao
uhuh
uw
er
er
iyiy
ihih
aeae
ao
uh
uwuw
erer
iyiy
ih
ih
eh
eh
ae
ae
ah
ao
uh
uwuw
er
iyiy
ih
ih
eh
eh
ae
ahah
aa
ao
uh
uh
w
uw
er
er
iy
ihih eh
ae
ah
aa
ao aouw
er
iyiy
ihih eh eh
h
aa aa
ao
uhuh
w
uw
er er
iy
iy
i eheh
ae
ae
ah
ah aa
aoao
uw
w
er
er
iy
iy
ih eh
eh
aeae
ah ah
aa
ao
ao
uwuw
r r
iyiy
i
ih
eh
eh
ae
ae
ah
aaa
ao
uh
uh
uw
uw
erer
iyiy
ih
i
eh
eh
ae
ah
a
aa
ao
uh
uw
uw
er
r
iy
iy
ih
ih
eh
ae
ae
ahah aa
o
uh
uw
er
r
iyiy
ih
eh
ae ae
ah
ah aa
oo
uhuh
uw
er
er
iy
iy
ae
ah
o
uh
uw
uw
er
er
iy
iy
ih
ih
eh
ae
ae
ahah
uhuh
uw
er
iy
iy
i
ah
ah
aa
aa
ao
ao
uh
uh
uw uw
er
er
iy
iy
aeae
aa
uh
uw w
er
er
iy iy
ae ae
ah
ah
aa
uh
uh
uw
erer
iy
iy
ih
eh
ae
ae
aa
o
o
uh
u
uw
uw
er
er
iy
iy
aeae
ahah
aoao
uh
uh
uw
er
er
iy
iy
ih
eh
eh ae
ae
ah
ao
uh
uh
uw
uw
er
er
F1 (Hz)
F2

(H
z)
Bagging 10 C4.5 decision trees. Misclassification error: 20.33%
0 200 400 600 800 1000 1200 1400
500
1000
1500
2000
2500
3000
3500
4000
Fig. 13. Decision boundaries and errors obtained by bagging 10 decision trees (number 9 in Table VIII).
Another approach for circumventing limitations of classifiers is to build ensembles with
methods as boosting or bagging. Fig. 13 illustrates how bagging can improve results, obtaining
decision boundaries not as limited as the ones of the basic decision tree in Fig. 9. There is even a
non-contiguous region for ER in Fig. 13, similar to the one suggested by the K-nearest neighbor of
Fig. 10, which obtained the best result in terms of classification based only on F1 and F2.
7. Conclusions
This report reviewed the work described in [1]. The concepts of formants and
fundamental frequency were discussed in order to avoid confusions with the nomenclature F0 and
F1-F3. A flexible partition of the database was proposed, such that results obtained by different
researchers can be easily compared. Results of vowel classification experiments conducted with
Weka were presented, with some plots on the F1 x F2 plane to help interpreting results.
References
[1] G. Peterson and H. Barney, "Control methods used in a study of vowels," Journal of the Acoustical Society
of America, vol. 24, pp. 175-184, 1952.
[2] R. L. Watrous, "Current status of Peterson-Barney vowel formant data," Journal of the Acoustical Society of
America, vol. 89, pp. 2459-60, 1991.
[3] E. Frank and e. al, "Weka [http://www.cs.waikato.ac.nz/ml/weka/]," The University of Waikato, 2002.
[4] A. Klautau, "http://speech.ucsd.edu/aldebaro/repository," 2002.
[5] C. L. Blake and C. J. Merz, "UCI Repository of machine learning databases
[http://www.ics.uci.edu/~mlearn/MLRepository.html]." Irvine, CA: University of California, Department of
Information and Computer Science, 1998.
[6] L. Rabiner and R. Schafer, Digital Processing of Speech Signals: Prentice-Hall, 1978.
[7] A. M. Kondoz, Digital Speech: Coding for Low Bit Rate Communication Systems: John Wiley & Sons,
1994.
[8] X. Huang, A. Acero, and H.-W. Hon, Spoken language processing, 1 ed: Prentice-Hall, 2001.
[9] R. A. Jacobs, M. I. Jordan, S. J. Nowlan, and G. E. Hinton, "Adaptive Mixture of Local Experts," Neural
Computation, vol. 3, pp. 79-87, 1991.
[10] R. S. Shadafan and M. Niranjan, "A dynamic neural network architecture by sequential partitioning of the
input space," Cambridge University, Cambridge May 13 1993.
[11] P. Clarkson and P. J. Moreno, "On the use of support vector machines for phonetic classification," presented
at IEEE International Conference on Acoustics, Speech, and Signal Processing, 1999.
[12] G. Fant, Acoustic theory of speech production, 1 ed: Mounton & CO, 1960.
[13] S. Stevens and J. Volkman, "The relation of pitch to frequency," Journal of Psychology, vol. 53, pp. 329,
1940.
[14] R. K. Potter and J. C. Steinberg, "Toward the specification of speech," The Journal of the Acoustical Society
of America, vol. 22, pp. 807-820, 1950.
[15] K. N. Stevens, Acoustic Phonetics. Cambridge, Mass.: The MIT Press, 1999.
[16] R. Kent and C. Read, The Acoustic Analysis of Speech: Singular, 1992.
[17] J. L. Flanagan, Speech Analysis, Synthesis and Perception. New York: Springer, 1972.
[18] P. Ladefoged, A Course in Phonetics, 4 ed: Harcourt Brace, 2001.
[19] A. Klautau, "ARPABET and the TIMIT alphabet [http://speech.ucsd.edu/aldebaro/papers]," 2001.
[20] P. Ladefoged,
"http://hctv.humnet.ucla.edu/departments/linguistics/VowelsandConsonants/course/chapter2/amerenglishvowels.html,"
2002.
Appendix - Command lines for Weka
# Algorithm Weka's command line
1 Naïve Bayes - simpler implementation weka.classifiers.NaiveBayesSimple
2 Naïve Bayes weka.classifiers.NaiveBayes
3 Naïve Bayes with kernel estimation weka.classifiers.NaiveBayes -K
4 Kernel density estimator weka.classifiers.KernelDensity
5 K-nearest neighbor with K = 5 weka.classifiers.IBk -K 5 -W 0
6 KStar weka.classifiers.kstar.KStar -B 20 -M a
7 Multilayer perceptron weka.classifiers.neural.NeuralNetwork -L 0.3 -M 0.2 -N 500 -
V 0 -S 0 -E 20 -H a
8 C4.5 decision tree with reduced error pruning weka.classifiers.j48.J48 -R -N 3 -M 2
9 Bagging 10 iterations using C4.5 with
reduced error pruning
weka.classifiers.Bagging -S 1 -I 10 -P 100 -W
weka.classifiers.j48.J48 -- -R -N 3 -M 2
10 Bagging 50 iterations using C4.5 with
reduced error pruning
weka.classifiers.Bagging -S 1 -I 50 -P 100 -W
weka.classifiers.j48.J48 -- -R -N 3 -M 2
11 AdaBoost M1 using C4.5 without reduced
error pruning
weka.classifiers.AdaBoostM1 -P 100 -I 10 -S 1 -W
weka.classifiers.j48.J48 -- -C 0.25 -M 2
12 AdaBoost M1 using C4.5 with reduced error
pruning (only approximately 4 iterations were
completed)
weka.classifiers.AdaBoostM1 -P 100 -I 10 -S 1 -W
weka.classifiers.j48.J48 -- -R -N 3 -M 0
13 Boosted stumps with LogitBoost weka.classifiers.LogitBoost -P 100 -I 10 -W
weka.classifiers.DecisionStump --
14 10 binary classifiers (one-against-all): SVM
with polynomial kernel of order 5
weka.classifiers.MultiClassClassifier -E 0 -R 2.0 -W
weka.classifiers.SMO -- -C 1.0 -E 5.0 -A 1000003 -T 0.0010
-P 1.0E-12 -O
15 10 binary classifiers (one-against-all): 50
iterations of AdaBoost using stumps
weka.classifiers.MultiClassClassifier -E 0 -R 2.0 -W
weka.classifiers.AdaBoostM1 -- -P 100 -I 50 -S 1 -W
weka.classifiers.DecisionStump --
16 10 binary classifiers (one-against-all): 50
iterations of LogitBoost using stumps
weka.classifiers.MultiClassClassifier -E 0 -R 2.0 -W
weka.classifiers.LogitBoost -- -P 100 -I 50 -W
weka.classifiers.DecisionStump --
17 10 binary classifiers (one-against-all):
multilayer perceptron
weka.classifiers.MultiClassClassifier -E 0 -R 2.0 -W
weka.classifiers.neural.NeuralNetwork -- -L 0.3 -M 0.2 -N
500 -V 0 -S 0 -E 20 -H a
18 20 binary classifiers (random code):
multilayer perceptron
weka.classifiers.MultiClassClassifier -E 1 -R 2.0 -W
weka.classifiers.neural.NeuralNetwork -- -L 0.3 -M 0.2 -N
500 -V 0 -S 0 -E 20 -H a
19 20 binary classifiers (random code): 100
iterations of AdaBoost using stumps
weka.classifiers.MultiClassClassifier -E 1 -R 2.0 -W
weka.classifiers.AdaBoostM1 -- -P 100 -I 100 -S 1 -W
weka.classifiers.DecisionStump --
20 20 binary classifiers (random code): 100
iterations of AdaBoost using multilayer
perceptrons
weka.classifiers.MultiClassClassifier -E 1 -R 2.0 -W
weka.classifiers.AdaBoostM1 -- -P 100 -I 10 -S 1 -W
weka.classifiers.neural.NeuralNetwork -- -L 0.3 -M 0.2 -N
500 -V 0 -S 0 -E 20 -H a
Appendix - F1 x F2 plots
0 200 400 600 800 1000 1200 1400
500
1000
1500
2000
2500
3000
3500
4000
iy
iy
ihih
eh
eh
ae
ae
ahah
aa aa
ao ao
uhuhuw
uw
er
er
iy
iy
ihih
eheh
ae
ae
ahahaaaa
aoao
uh
uh
uwuw
er
er
iy
iy
ihih
eheh ae
ahah
aa a
aoao
uh
uh
uwuw
erer
iy
iy
ih
ih
eh
eh
aeae
ahah aa aa
a
uhuhuw
uw
erer
iyiy
i
ih eh
eh aeae
ah
ah aa
aa
ao
uhuh
uw
erer
iyiy
ihi
eheh
ae ae
h
aa
ao
ao
uhuh
uw
uw
erer
iyiy
ihih
eheh aeae
ahah
a
ao
ao
uhuh
uwuw
er
er
iy
iy
ihih eh
eh
ae
a
ahah
aaa
aoao
uh
uw
erer
iy
iy
ihih
eh
eh
ae ae
ah ah aaaa
ao
ao
uhuhuw
uw
er
er
iyiy
ih
i
eheh
aeae
ah
ah
aa
aa
aoao
uh
uw
uw
erer
iy
ihih
eh
eh
aeae
ahah
aaaa
aoao
uhuh
uw
er
er
iyiy
ihih
eheh
aeae
ahh aaaa
ao
uh
uh
uwuw
erer
iyiy
ih
ih
eh
eh
ae
ae
ah
h
aa
ao
uh
uwuw
er
er
iyiy
ih
ih
eh
eh
ae
ahah
aoao
uhuh
uw
er
er
iy
ihih eheh
aeae
ahah
aa aa
ao ao
uh
uh
uwuw
r
er
iy
iy
ihih
eh
eh
ae
ae
ah ah
aa
aa
o o
uh
uw
uw
er
er
iy
iy
ih
ih
eh
eh
ae
ae
ahah
aa
a
aoao
uhuh
uw
uw
er
iy
iy
ih
ih
eh
eh
ae ae
ah
ah
aa
aa
ao
o
uh
uh
uw uw
er
er
iy
iy
ihih
eh
eh
aeae
ah
ah
aa
aa
aoao
uh
uh
uw w
er
er
iyiy
ihih
eh
ehaeae
ahah aa
aoao
uhuw
er
r
iiy
ihih
h
ae
ahah
aa
aoa
hu
rer
iyiy
i ih
ae
ahah aaa
ao
ao
uhuh
uw
er
er
iyiy
ihih
eheh ae
aah aa
a
aoao
uhuh
uw
uw
erer
iyiy
ihih
eh
aeae
a
aoao
uh
uwuw
erer
iyiy
ih
ih
eheh
ae
ahah a
aoaouwuw
erer
iy
iy
ih
ih eeh
ae
ae
ahh
aaa
ao
aouhuhuw
er
er
iy
iy
ihih
eh
eh ae
ae
ahah
aaaa
aoo
uhuhuu
err
iyiy
ihih eh eh
aeae
ah
h
aa aa
ao
uhuh
w
uw
er er
iy
iy
ii eheh
ae
ah
a aa aa
aoao
uh
uh
uw
w
er
er
iy
iy
ihi eh
eh
aeae
ah ah
a
a
ao
ao
uh
uwuw
r r
iyiy
i
ih
eh
eh
ae
ae
ah
aa
ao
uh
uh
uw
uw
erer
iyiy
ih
ih
eh
eh
ae
ah
aa
ao o
uh
uw
uw
er
r
iy
iy
ih
i
eh
eh
ae
ae
ahah aa
oo
uh
uw
er
er
iyiy
ihi
eheh
ae ae
ah
ah aaa
oo
uhuh
u uw
er
er
iy iy
ihih
eh
eh
ae ae
ah
ah
a
aa
ao
uh
uh
uw
uw
erer
iy
iy
ih
ih
eh
eh ae
ae
ah ah aa
ao
o
uh
u
uw
uw
er
er
iy
iy
ih
i
eh
aeae
ahah
aaaa
aoao
uh
uh
uuw
er
er
iy
iy
ihih
eh
eh ae
ae
ah
ah
aa
aaaoo
uh
uh
uw
uw
er
er
iyiy
ihih
eh ae
ae
ahah
a
a
h
uh
uwuw
erer
iyiy
ihih ehh
aeae
ah
aoao
uhuh
uwuw
er
er
iyiy
ihih
ehe
aeae
ah
auhuwuw
erer
iy
ih
eh
e
ae
ah
a
ao
uhuh
uuw
er
er
iy
i ih
eh
ae ae
ah
aauh
uwuw
erer
iy iy ih
i
eheh aeae
ahh
aouhuh
uwuw
iyiy
i
ih eheh
ae
e
ah
ah aa
ao
uh uh
uw
rr
iy
iih
eh ae
ae
a
a
a
ao
aoh
uw
r
er
iyiy
i ih
eh
eh
ae
ae
ah h
aa
aoao
h
h
r r
iyiy
ih
ih
eh
eh
eae
ah
ao
h
uh
uw
w
err
iyiy
ihi
aeae
ah
a
aoao
uhuh
uwuw
erer
iyiy
ihi
eh
ae
ae
hh
aa
uhuw
erer
iy i
ih
ih
eheh
aeae
ah
a
aa
a
o
uw
rr
iyi
ihih
eheh
ae
ae
ah
ah
aa
aa
o
ao
uhuh
w
uw
r r
i
iy
ihi
eh
ae
ae
ahah
aa
ao
uh h
uw
er
er
iy
iy
ihi
eheh
ae ae
a
o
ao
uhuh
er
iy
iy
ih
ih
eheh
aeae
ahh
aa
aa
ao
o
uh
w
uw
r
iy
ih ih
eh
eh
ae
ae
ah ah
a
aa
o
ao
uh
uh
w
uw
erer
iyiy
ih ih
eheh
ae ae
ah
ah aa
aah
uh
uw
uw
r
i
iy
ih ih
eh
eh
ae
ah
huw
uw
er
i
i
eh
aeae
a
uw
erer
iyiy ih
ih
eeh
ae
ah
aauhuh
er
er
iyiy
ihih eh
ae
ah
a
uuw
erer
iyiy ihih
eh
ae
ah aaa
ao
uhh
er
iiy
iih ehaeae
ah a
ao
uw
er
er
iyi
ihi eh
eh
ae
h
a o
w
er
i
iy
ih
ih
ae
ah
a
uu
r
iyiy
i
i
eheh
ae
ae
ah
uw
er
iyi
ihi eh
eh
aeae
a
h
uh
r
iy i
i eh
ae
ah
ah
aa
aoo
uh
uhuw
er
er
iy
iy
ihi
eh
eh aea
ah h
a
o
uh
uw
er
iy
iy
ih
ih eh
aeae
ah
aaaa
uh
uhw
w
rer
iyiy
ihih
eheh
ae
ae
aa
ao
ao
w
r r
iyiy
ih h
eheh
ae
ae
ah
aa
aa
uwu
erer
iiy
ihi
eh
ae ae
ah
aa
a
ao
u
uwuw
er
iyiy
ih
ih
ehe
ae
ae
ahah
aa
aa
ao
uh
uw
uw
rer
iyiy
ih
i
ae
ae
ah
ah
aa a
o
ao
uhuh
uw
w
erer
i
iy
ih
ih
eh
eh
ae
ah
ah
aaa
aoao
uh
uw
uw
err
F1 (Hz)
F2

(H
z
)
All 1520 vowels from [Peterson & Barney]
Fig. A.1- F1 x F2 for all 1520 vowels. This plot should be the same but for unknown reason it
seems to differ from [6], page 44.
0 200 400 600 800 1000 1200 1400
500
1000
1500
2000
2500
3000
3500
4000
iy
iy
ihih
eh
ae
ahah
aa aauhuhuw
uw
er
er
iy
iy
ihih
eh
ae
ae
aaaa
aoao
uh
uh
uwuw
er
er
iy
i
ihih
eheh
ae
ah
aa a
aoao
uh
uh
uw
erer
iy
iy
ih
eh
eh
aeae
ah
aa aa
o
uhuhuw
uw
erer
iyiy
i
ih eh
eh aeae
ah
ah aa
ao
uhuh
uw
erer
iy
iy
ihih
eheh
ae ae
ah
uhuh
uw
uw
err
iyiy
ih
eh aeae
ah
aa
ao
ao
uw
er
er
i
ih
ahah
ao
uh
uh
u
uw
erer
iy
ihih
eh
eh
ae ae
ah ah aa
ao
uhuhuw
er
er
iyiy
ih
ih
eheh
ae
ae
ah
ah
aa
aa
ao
uh
uw
uw
erer
iy
ih
aeae
ah
aaaa
ao
ao
uhuh
uw
er
er
iyiy
ihih
aeae
ao
uh
uwuw
erer
iyiy
ih
ih
eh
eh
ae
ae
ah
ao
uh
uwuw
er
iyiy
ih
ih
eh
eh
a
ae
ahah
aa
ao
uhuh
w
uw
er
er
iy
ihih eh
ae
ah
aa
ao aouw
er
iy
iy
ae
ah
o
uh
uw
uw
er
er
iy
iy
ih
ih
eh
ae
ae
ahah
uhuh
uw
uw
er
iy
iy
ih
ah
ah
aa
aa
ao
ao
uh
uh
uw uw
er
er
iy
iy
aeae
aa
uh
uw w
er
er
iyiy
ihi
eh
ehae
ah aa
aoao
uhuw
er
r
ii
ihih
h
ae
ahah
aa
ao
u
er
er
iyiy
i ih
ae
ah
ao
uhuh
uw
er
er
iyiy
ihih
eheh aeae
auhuh
uw
uw
erer
iyiy
ih
ae
ah
aoao
uh
uwuw
erer
iyiy
eheh
aoaouwuw
erer
iy
iy
ih
ih
ae
ahah
ao
aouhuhuw
er
er
iy
iy
ihih
eh
eh ae
ae
ahah
aaaa
uhuh
err
iyiy
ihih eh eh
ah
aa aa
ao
uhuh
uwuw
er er
iy
iy
i eheh
ae
ae
ah
ah aa
aoao
uw
w
er
er
iy
iy
ih eh
eh
aeae
ah ah
aa
ao
ao
h
uwuw
r r
iyiy
i
ih
eh
eh
ae
ae
ah
aaa
ao
uh
uh
uw
uw
er
er
iyi
ih
i
eh
eh
ae
ah
aa
ao a
uh
uw
uw
er
r
iyiy
ih
i
eh
ae
ae
ahah aa
o
uh
uw
er
r
iyiy
ih
eheh
ae ae
ah
ah aa
oo
uhuh
u uw
er
er
iy iy
ae ae
ah
ah
aa
uh
uh
uw
erer
iy
iy
ih
eh
ae
ae
h
aa
o
o
uh
u
uw
uw
er
er
iy
iy
aeae
ahah
aoao
uh
uh
uw
er
er
iy
iy
ih
eh
eh ae
ae
ah
ao
uh
uh
uw
uw
er
er
F1 (Hz)
F2

(H
z
)
Training set of unanimously identified vowels
Fig. A.2- F1 x F2 for training set with only
unanimously identified vowels.
0 200 400 600 800 1000 1200 1400
500
1000
1500
2000
2500
3000
3500
4000
iyiy
ihih
eheh ae
ae
ah
aa
ao
ao
uh
uh
uwuw
erer
iyiy ihih eh
aeae
ahah
aoao
uh
uwuw
er
er
iyiy
ihih
ao
uwuw
erer
iyiy
ih
ih
ae
ae
ah
a ao
uhuh
uwuw
er
er
iy
iy
ih
eheh
ae ae
ah
aa
ao
uh
uwuw
erer
iy iy
aeae
aa
uh
uwuw
erer
iyiy
i
ih
ae
aa
ao
uh uh
uuw
erer
iyiy
ihih
ae
ae
ah
aa
ao
aouh
uh
uwuw
er
er
iyiy
ih
eh
eh
ae
ae
aaaa
aoao
uh
uh
uwuw
er er
iyiy eh
eh
ae
ahah
aoao
uh
uw
uw
erer
iy
ihih
eheh
aeae
h
ah
aa
aa
aoao
uhuh
uwuw
er
er
iyiy
ih
eheh
ae
ah
aaaa
ao
uhuw
er
iy i
ih
ih
eh
ah
ah
a
aa
uh
uw
erer
iyiy
ihih
eh
ae
ae
ah
ah
aa
aa
ao
aouwuw
er er
iy
iy
ihi
eh
eh
ahah
aa
ao ao
uh uh
uwuw
er
er
iy
iy
ihi
eheh
ae ae
ah
ao
ao
uhuh
uw
er
iy
iy
eh
aeae
ahah
ao
ao
uh
uh
uw
uw
er er
iy
ih ih
eh
eh
ae
ae
ah ahuh
uh
uw
uw
erer
iyiy
ih ih
eh
ae ae
ah aa
aa
ao
uh
uh
uw
uw
er
eriy
ih ih
eh
eh
ae
ah
ah
uh uhuw
uw
er
i
i i
eh
ae
ahah
ao
ao
uh
uw
uw
erer
iyiy ih
i
eae
ah
aa
aa
ao
uh
uw
er
er
iyiy
ihih eh
ae
ae
ah aa
o
uhuh
uwuw
r
iyiy
aeae
ah a
uhuh
uwuw
er
iy
ihih eh ae
aa
uw
uw
er
er
iiy
ih eh
eh
aeae
a a
ao
uh
uw
er
i
iy
ih
ih
ae
ae
ah
a
a
ao
uh
uuw
erer
i iy
eh
ae
ae
aah
a auhuh
uw
erer
ii
ihi
eh
ae
ae
ahah aaa
h
uh
uw
er
iy iy
ah
ah
aa
ao
uh
uhuw
er
er
i
iy
ihi
eh
eh
ah
aaaa
oo
uh
wuw
er
iy
iy
aeae
ah
ao
uw
uw
rer
iyiy
ihih
eheh
ae
ae
ah
aa
ao
ao
uw
er r
iyiy
ih ih
eheh
ae
ae
ah
a
uh
uw
erer
iyiy
ihih
ae ae
ao
h h
uwuw
er
iyiy
ih
ih
eheh
ae
ae
ahah
aa
aa
ao
uh uh
uw
uw
erer
iyiy
ih
i
ae
ae
ah
a
uh
uw
erer
iy
ih
ih
eh
eh
ae
ae
ah
ah
aa
aoao
uh
uh
uw
uw
err
F1 (Hz)
F2

(H
z
)
Testing set of unanimously identified vowels
Fig. A.2- F1 x F2 for testing set with only