Classification of Peterson & Barney’s vowels using Weka Aldebaro Klautau UC San Diego – EBU – I La Jolla, CA 92093-0407 Email: [email protected] 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 LAR is a well-known, but outdated parameterization of speech [6].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