MEASUREMENT OF SOME CHARACTERISTICS OF VOWEL SOUNDS

V. P. BONDARENKO, V. A. BONDAR

(Presented by the Department of Computer Engineering)

As is known [1, 2, 3], the energy in the spectrum of the speech signal of vowel sounds is concentrated mainly in the formant regions. Consequently, the energy spectrum of the signal can be represented as a sum

\[ S(\omega)=\sum_{i=1}^{n} S_i(\omega), \tag{1} \]

where \(S_i(\omega)\) is the envelope of the energy spectrum of the \(i\)-th formant, and \(n\) is the number of formants.

It may be assumed [1, 2, 3] that the spectral width of the \(i\)-th formant does not exceed one octave. In this case, expression (1) for a particular signal can be written in the form [4]

\[ f(t)=\sum_{i=1}^{n} f_i(t)=\sum_{i=1}^{n} A_i(t)\sin \int \omega_i(t)\,dt. \tag{2} \]

To obtain the sum (2), it is sufficient to pass the signal through a system of filters. The filter parameters for undistorted transmission of the amplitude \(A_i(t)\) and frequency \(\omega_i(t)\) must satisfy the condition of quasi-stationarity [5, 6], and at the same time their quality factor must not be less than unity [4].

Thus, in the analysis of speech signals of vowel sounds it is sufficient to know the functions \(A_i(t)\) and \(\omega_i(t)\). The upper frequency component of the function \(A_i(t)\) at the output of a filter, transmitted by it without distortion, is determined by its passband \(\Delta\omega_i\) at the level 0.7, and the upper frequency of the function is determined from the expression [5, 6]

\[ \Delta\omega_i \geq 5\sqrt{\Delta\omega\,\Omega_i}, \tag{3} \]

where \(\Delta\omega\) is the frequency deviation of the signal \(f_i(t)\), and \(\Omega_i\) is the upper frequency component of the function \(\omega_i(t)\).

For small frequency deviation, as follows from (3), the filter can transmit without distortion a fairly wide spectrum of the frequency-modulating function.

For vowel sounds, as noted by a number of authors [1, 2, 4, 7], there is a change in the formant frequencies, i.e., a deviation of the carrier frequency. In a number of works [1, 7] it is assumed that the spectrum of the frequency-deviation law is rather broad, while in [4] it is asserted that it is limited to a frequency of 50–60 Hz.

As is known [8], for a small index of frequency modulation the bandwidth of the signal spectrum is equal to twice the bandwidth of the spectrum of the modulating function, while the amplitude of the side frequencies is proportional to half the modulation index and to the amplitude of the carrier. The bandwidth of the signal spectrum measured at the 0.7 level may turn out to be narrow and to be determined mainly by slow changes in the amplitude of the carrier frequency. The total width of the spectrum at a lower level will be rather broad, as is the case for the spectra of vowel sounds [3].

To verify this proposition, the following measurements of the parameters of vowel-sound signals were carried out. The signal was passed through filters with resonant frequencies of 800 and 1600 Hz and with a quality factor equal to unity. At the filter output the signal was clipped, and then each time interval between two zeros was measured.

The number of identical time intervals was stored and then, after the end of the sound, recorded. Thus, at the output of the recording device one obtained the distribution of periods by duration, or by frequency.

Fig. 1

Figure 1 presents a typical distribution of instantaneous frequencies for the first formant of the sound “A.” Each point corresponds to a definite frequency. The frequency values by point number from left to right are presented in the table.

Thus, the frequency deviation is approximately 200–300 Hz, with an average frequency of about 700 Hz, i.e., the frequency deviation is 25–30%, which confirms the possibility of the existence of a broad spectrum of the modulating function. It is natural to expect that the law of frequency modulation may contain useful information about the phoneme.

Table

To verify this supposition, measurements were made of the law of frequency modulation of the first formant.

The time interval between two zeros of the filtered and clipped signal was converted into the amplitude of a sawtooth voltage. The obtained voltage and the filtered signal were recorded by a multichannel oscillograph on motion-picture film at a speed of 1 m/sec.

Figure 2 gives one of the oscillograms for the phonemes “A” (upper curves) and “O” (lower curves). It was observed that the law of meas—

frequency measurement for vowel sounds over a period of the fundamental tone is, in general, repeated and agrees fairly well in approximately 50–70% of cases for different speakers. There is a significant difference in the laws of frequency change from phoneme to phoneme.

Fig. 2

The low accuracy of measurement, which is mainly explained by the discreteness of the readouts, and the small number of speakers (5–6 per phoneme) do not allow a final conclusion to be drawn.

From the studies presented it is clear that, in a speech signal, the frequency of the formants changes over time even during a period of the fundamental tone, and the law of frequency change carries a certain informational load about the phoneme. This means that, with this approach to signal analysis, the filters must have a low quality factor and a constant slope of the phase characteristic, so as not to distort the laws of frequency and amplitude modulation. The noted requirements for the filters, in turn, coincide with the parameters of the basilar membrane [2].

REFERENCES

1. M. A. Sapozhkov. The Speech Signal in Cybernetics and Communications. Svyazizdat, 1963.

2. J. Flanagan. Analysis, Synthesis, and Perception of Speech. Izd. “Svyaz,” 1968.

3. E. T. Semenova. Analysis of features for speech recognition. In: Bionics, “Nauka,” 1965.

4. I. T. Turbovich, O. N. Petrov. On one method of complete description of one-dimensional images by a set of simple functions (as applied to speech signals). In: Pattern Recognition. Theory of Information Transmission, Publishing House of the Academy of Sciences of the USSR, Institute for Problems of Information Transmission, 1965.

5. A. S. Vinnitskii. Modulated Filters and Tracking Reception of FM. Izd. “Sov. radio,” 1969.

6. S. V. Person. Nonlinear distortions in the amplification of FM oscillations. Radiotekhnika, vol. 6, No. 6, 1951.

7. Caigwell P. Smith, Vokal Respons Synthesizer. The Jornal of the Acoustical Society of America. V. 37, No. 1, 1965.

8. N. S. Gonorovskii. Radio-Engineering Circuits and Signals. Part I. Izd. “Sov. radio,” 1967.