Foundations of Language Science and Technology. Acoustic Phonetics 1: Resonances and formants
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1 Foundations of Language Science and Technology Acoustic Phonetics 1: Resonances and formants Jan 19, 2015 Bernd Möbius FR 4.7, Phonetics Saarland University
2 Speech waveforms and spectrograms A f t
3 Formants Spectral peaks, energy maxima: formants Formants emerge as a consequence of selective reinforcement of certain frequency ranges, corresponding to resonance characteristisc of the vocal tract. Distinguishing between voice source (periodic, stochastic, transient, mixed excitation) and sound formation in the vocal tract motivates the source-and-filter model of speech production. References: Gunnar Fant (1960): Acoustic theory of speech production Gerold Ungeheuer (1962): Elemente einer akustischen Theorie der Vokalartikulation
4 Source-filter model of speech production
5 Vocal tract as acoustic filter Vocal tract geometry, determined by tongue position, jaw opening, and lip protrusion
6 Vocal tract: acoustic tube model [Clark et al., 2007a, p.241]
7 Vocal tract: acoustic tube model Acoustic signals evolve as longitudinal waves in vocal tract 2 physical parameters of acoustic waves sound pressure p : change of air pressure evoked by sound at place of measurement sound velocity v : speed of air particles caused by sound event (note: this is not the speed of sound c!) Perfect reflexion at sound-hard (lossless) walls of tube v = 0 at place of reflexion (Lossy) reflexion at sound-soft transition from vocal tract to free acoustic field (i.e. from lips to air) p = 0 at place of radiation
8 Sound pressure waves in vocal tract [Hess, ms.]
9 Computing formant frequencies Resonance frequencies of neutral vocal tract computed as speed of sound divided by wave length: f i = c / λ i Frequencies of resonances/formants: F1 = 340 / (4 * 0.17) = 340 / 0.68 = 500 Hz F2 = 340 / (4/3 * 0.17) = 3 * 340 / (4 * 0.17) = 1500 Hz F3 = 340 / (4/5 * 0.17) = 5 * 340 / (4 * 0.17) = 2500 Hz Distribution of formant frequencies in neutral vocal tract corresponds to formants of central vowel [ǝ] Simple tube model, with constant area, is inadequate for computing formants of other vowels (cf. acoustic theory of vowel articulation [Ungeheuer 1962])
10 Tube model with variable area [Clark et al., 2007a, p.246]
11 Resonances: standing waves parameter: v [Johnson, 1997, p.99]
12 Standing waves: interpretation interpretation of the graphical representation of standing waves in idealized vocal tract (neutral configuration, see previous figure): first 4 formants displayed (F F ) in tube model and in vocal tract places of maximum sound velocity (sound velocity nodes, V ) places of maximum sound pressure (wave maxima, "antinodes") localization of V in vocal tract
13 Dynamic area changes resonances of vocal tract with variable area cannot be straightforwardly visualized as in the neutral tube model local area changes affect frequencies of resonances, depending on energy distribution of standing wave in tube along longitudinal axis ("z-axis") e.g., constriction at lip end of tube has same effect as constriction at glottis end: lower resonance frequency acoustic vowel system can be interpreted as representing geometrical changes with respect to neutral tube geometry and resulting changes of resonance frequencies away from neutral values acoustic theory of vowel articulation [Ungeheuer (1962)]
14 Acoustic theory of vowel articulation
15 Vowels (IPA) F2 F1
16 Vowels (German [Pompino-Marschall, 1995])
17 Vowels (German [Möbius, 2001])
18 Vowels (German, F1/F2/F3 [Möbius, 2001])
19 Vowels (Am. English [Peterson and Barney, 1952])
20 Vowels (German [Möbius])
21 Vowels (German [Möbius])
22 Vowels (German [Möbius])
23 Vocal tract vs. lossless tube losses in the vocal tract caused by friction between air particles vibration of vocal tract walls viscosity of vocal tract tissue radiation of sound energy into free acoustic field lossy vibrations are damped exponentially spectral equivalent of damping: bandwidth defined as frequency range comprising 50% of power corresponding to decrease of amplitude by 3 db (or 0.707*A) sound energy expressed in [db] sound energy is proportional to square of amplitude 50% of power = energy maximum minus 3 db 0.5 * power = 0.5 * amplitude = * amplitude
24 Resonance response Formant parameters: frequency, amplitude, bandwidth
25 Speech waveforms and spectrograms B3=bandwidth(F3) B2=bandwidth(F2) B1=bandwidth(F1)
26 Thanks!
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