3 Acoustical Theory There is nothing more practical than a good theory The linear source-filter theory is one of the best in our fieldBased on Gunnar Fant’s “Acoustic Theory of Speech Production”The theory expresses articulatory-acoustic relationships
5 Acoustical Theory The source is vocal fold vibration for some consonants, the source is more complexcan be in the vocal tract or a combination of bothThe filter is the vocal tractextending from the vocal folds to the lips or nareslike all filters, the vocal tract is frequency dependent
6 Acoustic TheoryThe source and the filter are assumed to be independentthis is an assumption made for convenienceit implies that you can change the output of the vocal folds without changing the vocal tractvice-versa
7 Vowels Modeled as a tube closed at one end and open at the other the closure is a membrane with a slit in itthe tube has uniform cross sectional areamembrane represents the source of energy (vocal folds)the energy travels through the tubethe tube generates no energy on its ownthe tube represents an important class of resonatorsodd quarter length relationshipFn=(2n-1)c/4l
9 Vowels (2) There are an infinite number of resonances for this tube we need only consider the first three or fourthe model is valid to only about 5 kHzThe model was developed by Chiba and Kajiyama in 1941based on pipe organs for which a great deal was known
10 Vowels (3) If c=35000 cm/s, and l=17.5 cm What are the first three resonances?The simple tube closed at one end and open at the other, with the above length, is a reasonable approximation of /ᴧ/ produced by a male talker
11 Vowels (4) Some points to note: A curved tube (vocal tract) and a straight tube (model) behave identically acoustically out to 5 kHzthis is because the curve begins to affect acoustic signals with a short wavelengthThe resonances are equally spaced if the tube has uniform cross sectional areaRemember: all of the energy comes from the source (vocal fold vibration for vowels)Changing the length of the tube changes the resonance frequenciesInfluenced by age and sexl= 14.5 cm for femalesl= 8.75 cm for children
13 Vowels (5) A one-vowel model isn’t very useful Different vowels are modeled, acoustically, by different vocal tract shapesPhonetically, how are vowels distinguished?If we place a constriction in the tube (vocal tract)the resonances changesif you change the articulation, you change the vocal tract shape, and the resonance frequencies, amplitudes and bandwidths
15 Vowels (6) the amplitude of the harmonics decreases by -12 dB/octave The output energy of a vowel is the product ofthe source energythe size and shape of the resonatorthe radiation characteristicGlottal source characteristics for vowelsvocal fold vibration is periodicwhat does this imply for the spectrum?f0 or F0 is used to indicate the vocal fundamental frequencythe amplitude of the harmonics decreases by -12 dB/octave
20 Vowels (7) Filter characteristics for vowels the vocal tract is a dynamic filterit is frequency dependentit has, theoretically, an infinite number of resonanceseach resonance has a center frequency, an amplitude and a bandwidthfor speech, these resonances are called formantsformants are numbered in succession from the lowestF1, F2, F3, etc.A1, A2, A3, etc.B1, B2, B3, etc.the formants together form the transfer functioninput-output relationshipformants become physically evident only when energized
21 Vowels (8) Radiation characteristic acoustic effect when a sound leaves a small area and enters a large oneThe effect is to raise the slope of the spectrum by +6 dB/octaveAcoustic Phonetic Relationships for VowelsF1 is inversely related to tongue heightF2 is directly related to tongue advancementLip rounding lowers all formant frequencies
23 Vowels (9) Perturbation Theory Volume velocity variations reflect the way air particles vibrate at a particular point in the vocal tractAt some points, vibration is minimal (node); at others, maximal (antinodes)For F1, the antinode is at the open end and the node is at the closed endFor F2, there are two antinodes and two nodesFor F3, there are three antinodes and three nodesetc.
24 Vowels (10) Perturbation Theory (continued) if a change in cross sectional area is applied (a perturbation)the acoustic effect depends on proximity to a node or an antinodenear an antinode the formant frequency lowersnear a node the formant frequency riseslip constrictions lower all formant frequencieslaryngeal constrictions raise all formant frequencies
25 Vowels (11) Amplitude relationships amplitudes depend on formant frequenciesif F1 is lowered (raised), A1 lowers (rises)if two formant frequencies move closer together, then both peaks increase in amplitudehow do you raise or lower formant frequencies?
26 Vowels (12) Source-Filter Interactions Some vocal tract shapes may affect vocal fold vibrationSingers’ formantHigh impedance constrictions require greater subglottal air pressureVocal tract - vocal fold coupling during open phase of vibratory cycle
27 Consonants (1)The linear source-filter theory can be used to describe the acoustics of consonants as well as vowelsFor consonants, however, the source is not always at the level of the vocal foldssome sources are in the vocal tractthese sources are aperiodicdurations and amplitudes also are different from vowelsNonetheless, source-filter theory gives us a series of expectations for the acoustic characteristics for consonants
28 Consonants (2) Fricatives Modeled as a tube with a very severe constrictionThe air exiting the constriction is turbulentThe Reynold’s number gives the conditions for turbulenceRe=vh/ʊNotice that turbulence can be generated in two waysZeros or antiformants can be found in the spectrumBecause of the turbulence, there is no periodicity unless accompanied by voicingWhat does an aperiodic spectrum look like?
29 Consonants (3) When a fricative constriction is tapered the back cavity is involvedthis resembles a tube closed at both endsFn=nc/2lsuch a situation occurs primarily for articulation disorders
30 Consonants (4) Nasal consonants Velopharyngeal port is open and the oral cavity is completely blocked at some pointThe side-branch resonator produces antiformants (zeros)The overall vocal tract is longer than for vowelsWhat effect does this have on the spectrum?Oral formants, nasal formants, nasal antiformantsNasal murmur
31 Consonants (5) Stops The tube model is not altered very much for stops However, the time domain becomes criticalThere is a complete closure of the vocal tract somewherePressure builds up behind the closureRapid releaseThe articulation results in a burst and transitions
32 Consonants (6) Other consonants are variations of these Affricates LiquidsGlidesDiphthongs