24.910 Laboratory Phonology The source-filter model of speech productionI. Vowel inventoriesSourcesCues to vowel qualityCues to vowel qualityVowel qualityLow vowels [ɑ, a, æ] Low vowels [ɑ, a, æ] Non-low vowels (e.g. [i, e])Helmholtz resonatorsNon-low vowels - nomogramPerturbation Theory (Chiba and Kajiyama 1941) Perturbation Theory (Chiba and Kajiyama 1941) Perturbation Theory (Chiba and Kajiyama 1941) Perturbation Theory vs. two-tube models Lip roundingMIT OpenCourseWare http://ocw.mit.edu24.910 Topics in Linguistic Theory: Laboratory PhonologySpring 2007 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.24.910Laboratory PhonologyThe source-filter model of speech production• Readings for next week: – Ladefoged ‘Elements of Acoustic Phonetics (2nd edn) ch. 10 from p.160, ch. 11 to p.183.– Liljencrants & Lindblom (1972).• Note: Mel is an auditory frequency scale like the Bark scale.• Assignments (due 3/6):– Write up analysis of mandarin affricates.– Acoustics assignment.• Common vowel inventories:I. Vowel inventories i u i u i u e o e  o a a a Arabic, Nyangumata, Aleut, etc. Spanish, Swahili, Cherokee, etc. Italian, Yoruba, Tunica, etc. • Unattested vowel inventories: i i  i u e e    a a Why?ɔSpectrogram image removed due to copyright restrictions.See: http://hctv.humnet.ucla.edu/departments/linguistics/VowelsandConsonants/course/chapter8/8.3.htmSource-Filter Model of Speech Production4002000.1 0.2 0.3Output from lipsGlottal airflowTime (in secs)3030302020201010100000 1000 2000 3000500 25000 1000 2000 30001500Frequency (Hz)Frequency (Hz) Frequency (Hz)Source SpectrumOutput SpectrumResonances =Formant FrequenciesVocal TractFilter FunctionFigure by MIT OpenCourseWare.Sources• A source is an input of acoustic energy into the speech production system. • There are two basic types:– Voicing–NoiseVoicing source• Voicing is a periodic source produced by modulation of the airflow from the lungs by the vocal folds.(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)TracheaFalsevocalfoldsEpiglottisVocal foldsFigure by MIT OpenCourseWare. Figure by MIT OpenCourseWare.Voicing sourceVideo removed due to copyright restrictions. Please see “The vibrating vocal folds”in Peter Ladefoged’sVowels and Consonants.Video removed due to copyright restrictions. Please see “The vocal tract and larynx”to view.Voicing source• vocal fold vibration produces a complex periodic wave, whose spectrum contains energy at the fundamental frequency of laryngeal vibration and multiples of the fundamental frequency (harmonics).Figure by MIT OpenCourseWare. Adapted from Rothenberg, M. "The Glottal Volume Velocity Waveform During Loose and Tight Glottal Adjustments." Proceedings of the VII International Congress of Phonetic Sciences (1971): 380-388. 00.500.500.500.500msec100.5LITERS SECSPEAKER P.B.FUNDAMENTALFREQUENCYSUBGLOTTALPRESSURE107 Hz97 Hz94 Hz89 Hz83 Hz8.6 cm H2O8.4 cm H2O8.1 cm H2O7.3 cm H2O6.9 cm H2OGlottal volume velocity waveforms obtained by inverse-filtering the volume velocity at the mouth.From five successive repetitions of the phrase /bap/ (from top to bottom). Time in each trace runsfrom left to right. Waveforms traced from original.Noise source• Air turbulence generated at an obstruction involves random (aperiodic) pressure fluctuations over a wide range of frequencies. • Noise generated at the glottis is called aspiration, while noise generated elsewhere is called frication. 00 2 4 6 8 105 10 15 20 25302520151050kHzBarkAmplitude (dB)Acoustic frequency (kHz) and Auditory frequency (Bark)Power Spectrum of Turbulent Noise (Shadle 1985) Image by MIT OpenCourseWare. Adapted from Johnson, Keith. Acoustic and Auditory Phonetics. Malden, MA: Blackwell Publishers, 1997.SourceA sound may involve more than one source. • E.g. a voiced fricative combines voicing and frication noise• breathy voice can combine voicing and aspiration noise. • voiceless fricatives can have noise generated at the glottis and at the supralaryngeal constriction.Filters• The vocal tract acts as a filter, modifying the source waveform.• An acoustic filter is a device which passes or amplifies certain frequencies and attenuates others. • An important characteristic of a filter is its transfer function - the ratio of the output to the input depending on frequency.1.41.20.80.60.40.2100 0.1 0.2 0.3 0.4 0.5 0.6 0.7MagnitudeNormalized frequencyFIR High Pass Filter1.41.20.80.60.40.200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.01MagnitudeNormalized frequencyStopband FilterFigure by MIT OpenCourseWare. Figure by MIT OpenCourseWare.The vocal tract as a filter• The sound wave at some distance from the speaker is the result of filtering the source with the vocal tract filter, plusthe radiation characteristics of the lips/nose.• How does the vocal tract operate as a filter?• What determines the characteristics of the filter?Outline• Resonators are filters.• The column of air in the vocal tract is a resonator, hence a filter.• The characteristics of the filter depend on the shape of the vocal tract - we will explore the relationship by considering simple cases.Resonators• A body, like a mass of air in a tube, naturally vibrates at one or more frequencies. • If a pulse of energy is imparted to the air, it will vibrate at these natural frequencies. • If a source (driving force) which is vibrating at a natural frequency of the body is applied to it (e.g. a tuning fork is held over the tube of air), the body will resonate with the source, i.e. vibrate strongly at the same frequency. • If a source of a different frequency is applied to the body it will vibrate with less amplitude.Resonators• We can plot the response of a resonator to a range of input frequencies. Peaks mark the resonant frequencies.• Resonators vary in the range of frequencies they will respond strongly to¾ a sharply tuned resonator only responds strongly to frequencies very close to the resonant frequency (it has a narrow bandwidth).¾ A resonator with a wide bandwidth will vibrate strongly in response to a wider range of input frequencies.2000300 400 500 60095-105 175-225 350-550Figure by MIT OpenCourseWare. Adapted from Ladefoged, P. Elements of Acoustic Phonetics. 2nd ed. University of Chicago Press, 1996.Resonators are filtersA resonator acts as an acoustic filter:• Consider the