Dept. for Speech, Music and Hearing

Quarterly Progress andStatus Report

Notes on glottal flowinteraction

Fant, G. and Lin, Q. and Gobl, C.

journal: STL-QPSRvolume: 26number: 2-3year: 1985pages: 021-045

http://www.speech.kth.se/qpsr

Fig. 2. The same as Fig. 1, male subject L.N.

The reference vo is the velocity that is solved from the kinematic equation

r\

assuming short-circuit load and no glottal friction or inductance. With the combined entry and exit coefficient of the order of k=l and the density g = 1.14 g/cm3 we find,

i.e., 3709 cm/s at a transglottal pressure Ps = 8 cm H20. The ideal short-circuit flow is thus v A (t). Finite viscosity o g

causes a certain rounding of the corners of the pulse and the glottal inductance also adds some small effects to the corners.

The pressure drop across the glottal inductance is

which is a simpler expression than the usual decomposition in terms of U 'L + U L', i.e., a separate inductive and resistive term. As long as 9 g g 9 dx/dt is modest, as in the case of the major part of the short circuit pulse, the effect of glottal inductance is small. With a finite load, however, the glottal inductance gains some importance. Contrary to the statement of Ananthapadmanabha & Fant (1982), the effect is not negli- gible. We do not have any illustration in the present survey but a few controls have shown that the modulation depth of the interaction ripple is somewhat less and the excitation 0.5 dB less without the glottal inductance.

The velocity factor x(t) rises towards the end of the glottal open cycle and then drops. This profile is mirrored in the negative of the transglottal pressure, or rather its square root. Here is the origin of the pulse skewing as discussed by Rothenberg (1981a) and by Fant (1982). The sensitivity of x(t) to acoustic parameters is expressed by the product

where G' is the time derivative of glottal conductance and 1 L is the 9

total vocal -tract inductance. The skewing factor also relates to the deqree of interaction rip

ple. It is proportional to glottal rnaximurn area and overall inductance and inversely proportional to the duration of the glottal pulse and the square root of lung pressure.

STGQPSR 2-3/1985 - 26 -

UQ' 400

300

200

100

0

-100

-200 Fig. 3. Triangular glottal

-300 area function Glottal flow

-400 A c t )

flow derivative.

-so0

0 2 3 4 5 6 7 8 m s

DUG, A 1 = 1

Fig. 4. The same Ag (t ) as in Fig. 3. Dlff. glottal flow, single formant load f=500 Hz, B=50 Hz, L=5 mH.

Pulse skew in g .

~ Effect o f resonance

I I I I I I I - - - - ( ~,",y,tance u g

700

600

- 500 - - 400

- 300

- 200

- 100

load

II I 1 1 I - , 0 1 ? 3 ~ 1 5 6 m

(t), Fant type w i t h K=l in falling branch. Inductance 5 rnH. Flow and derivative w i t h and without capacitor in single resonant circuit load.

I , I

UG' , AGMAX=O. 3 CM2

dB . ~ g ' FFT + 6 dBIoct

- .

. - I I I I I I I I I

Fig. 6. Solid lines - flow and flow derivatives. Dotted line - supra- glottal pressure assuming single resonant circuit load. First pulse only.

There is a small but distinct time lag between the flow derivative negative peak and the F1 oscillation. The FFT of the glottal flow normalized by +12 d~/oct emphasis is calculated from the glottal flow derivative +6 d~/oct. There is a distinct minimum at 900 Hz. Figs. 7 and 8 illustrate the effects of varying lung pressure PI max glottal area Ago, and inductance L assuming F1 = 500 Hz and B1 = 50 Hz. The glottal-flow derivative peak amplitude increases somewhat more than proportional to %o which is explained by the additional skewing. In- crease in inductance alone increases the flow derivative pulse and, thus, the spectrum level at higher frequencies but the effect is margin- al only. An increase in the modulation depth of the interaction ripple in the time and frequency domain is, however, apparent.

The double peak in the flow derivative is further illustrated in Figs. 9 and 10. The peak distance decreases with increasing F1 as expected. There is an associated tendency of a spectral dip to occur sliglltly below 2F1. This dip is joined with a preceding peak which accounts for some extra spectra energy in this region. Fig. 12 shows the correlation of the reciprocal of the peak distance 1/T with F1. P

Fp = 1/T is somewhat lower than 2F1 as already exemplified. It P should be stressed that this relation is not as well preserved at high Fo phonations.

As illustrated in Fig. 13, the second pulse differs significantly from the first. Such superposition phenomena will be discussed in more detail later. Fig. 14 shows the effect of removing the viscosity term in the calculation of glottal flow derivative. The negative peak is reduced by 1 dB and the reduced ripple in the first pulse is also apparent. Fig. 15 illustrates conditions where the friction has a definite influence on the spectrum roll-off. This tendency is enhanced by low inductance and a relatively long glottal pulse, and a low sub- glottal pressure and a small Ago. Increasing the viscosity mfficient by a factor 4 provides a much faster spectral roll-off and there is no net gain of low-frequency spectrum level.

Glottal leakage is exemplified in Fig. 17. Here we have simply added a 0.05 cm2 constant value to our standard area function. The main effects of this differential change is to increase the F1 bandwidth from 50 Hz to 143 Hz. This value measured from the decay characteristics of the supraglottal pressure agrees exactly with what can be calculated from a simple model of extra parallel resistance loading the resonant circuit. There is a prominent remaining F1 oscillation in the maximally closed phase which should be retained after inverse filtering. The source spectrum does not attain any additional roll-of f. However, in practice the leaky voice, or rather a more abducted phonation as in aspiration and in the termination of voicing, is associated by a re- tardation of vocal-fold movements which accounts for a less pronounced discontinuity and, thus, a finite slope of the return phase of the flow derivative. As a result there should be an increased spectrum roll-off, see Fant (1985). Also the angular positioning of the vocal folds might contribute to the reduced discontinuity, see Childers & al. (1985).

Fig. 7a. Flow derivative. Various combinations of subglottal pressure P I max glottal area +O, and inductance L. First pulse only. Standard A&), Fant, K=l.

Fig. 7b.

9 0

0 1 2 3 4 kHz 0 1 2 3 4 kHz

Fig. 8. FET, +6 dB/oct of flow derivative. Various combinations of subglottal pressure P, max glottal area Ago, and inductance L. First pulse only.

A g ( t ) = Ago sin 2 n Fgt

Fig. 9. Flow derivative,various frequencies of resonant load. Sinusoidal Ag (t ) .

Fant Ag(t) K = l Fg=250

Fig. 10. Flow derivative, various frequencies of resonant load. Standard Fant, K=l, Ag(t).

130

F , = 400 120 Ago =0.2 L=5

p = 8 B= 50

Fant Ag(t) K=l Fg=250

x = Fant Ag(t1 K = i Fg= 250

o = sine wave Ag( t ) Rise time 2 ms

n = triangular Ag(t1

Fig. 11. FET, +6 d ~ / o c t of f l w derivatives, Fig. 12. Sumnary of f l w derivative double-peak Fig. 10. distance as a function of F1 resonant

load frequency. Rise time of area func- tion = 2 m s .

UG', N O ' F R I C T I O N UG',NORMAL F R I C T I O N

L = S Ago =0.2 P = 8 F=500 A g ( t ) = Fant K = l , Fg= 250

Fig. 13. Effect of r m i n g friction (Viscosity) tenn in fluw derivative calculations. First and second pulse. Ag(t) rise time 2 m s .

ug'

200 I I I I I I I I I -

- - - - - - - - -

! -

- t 4

I I Normal -

- I

- - -

I

- - -

e - -

- , - I - - I I I I 1 I I I I

0 1 2 3 4 kHz

4 - -

I - Normal viscos~ty

I I I i ---L-- I 0 1 2 .I

L_I 4 kHz

Fig. 15. Canbination of low %O, low L, and long flow pulse rise time enhances the spectrum roll-off due to the glottal viscosity term.

UG' FFT, 4::cFRI CT I ON

Fig. 16. The same as Fig. 15 but spectnan roll~f f enhanced by four times increased viscosity coefficient .

0 I 2 3 '?

STANOARD I NPUT . I<I-12

STL-QPSR 2-3/1985 - 37 -

Fig. 17a. Glottal leakage exemplified by adding 0.05 an2 to % (t) .

UG' FFT, O.OSCM2, LEA!<

Fig. 17b. FFT (+6 dB/&) of f l w derivative, leaky case, Fig. 17a.

I We shall now return to the superposition effects, first with a

I single resonant load, Fig. 18, and then in Figs. 19-23, the complete I i vowel [ @ ] modeled from a three-tube approximation. As seen in Fig. 19,

when P1 = 2F0 and the duration of the closed phase is short and the bandwidth of B1 is low, the second and third flow pulses become reduced in amplitude but gain in excitation power, as evidenced by the increase of flow derivative amplitude and the associated increased spectral level. On the other hand, when F1 is close to 2.5 Fo, the situation is reversed; the second and third pulses gain in amplitude and the exci- tation is less than in the F1 = 2F0 case. These results confirm the earlier findings of Fant & Ananthapadmanabha (1982) and of Rothenberg (1981b) .

The soprano voice An even more apparent interaction along the same lines has been

discussed by Rothenberg (1985). We have attempted to reconstruct the experimental data of his figure 3 pertaining to a soprano singing with F1 close to Fo. My mcdel was a single resonancz load interactively con- nected to the time-variable glottal impedance. The following parameters were adopted: F = 714 Hz, F1 = 740 HZ, B1 = 75 HZ, L = 5 mH, P = 8 cm H20, Ago = 0.1 cm9. glottal depth 0.2 cm, glottal length 1 cm. duration of open period 0.9 ms, rise and fall time 0.45 ms. duration of closed period 0.5 cm, and open quotient 0.64. The pulse shape was a raised cosine for the opening branch, as in the Fant mcdel, and a single cosine for the closing part. Calculations were carried out at a sampling frequency of 40 kHz. As can be seen in Fig. 24, the second and third pulses carry a much smaller volume flow than the first pulse. This is apparentlydue tothe coincidence of high supraglottal pressure with glottal opening. The third pulse resembles ~othenberg's figure 3 and would do so even better, if we had chosen L = 4 mH. A value of L greater than 6 mH would have created brief intervals of negative flow. The appearance of a factor 1 xlx instead of x2 in Eq. (6) allows for a negative flow.

The case of F1 = 1.58 Fo is illustrated in Fig. 25. Here a nega- tive supraglottal pressure build-up during the open phase tends to increase the glottal flow and thus the air consumption. Flow deriva- tives of the two examples are shown in Figs. 26 and 27. The main negative spike, responsible for the excitation level of higher formants, is somewhat but not much greater in the case of coincidence of F1 and

Fco*

General conclusions In studying interaction phenomena it is important to keep apart the

inherent effect within the first glottal pulse and the total interaction in a subsequence pulse. At high Fo the contributions from the previous h~story of the supraglottal pressure variations dominate and cause

-2000 1- , - I l l I

0 5 10 15 2 0 m s

A g ( t ) = Fant K=l Fg=250 Ao=O 2

ud( f ) P=8 vowel @I F0=149

1 pulse

2nd"

I I 9 1 L! I I I : : ' l !

2 1 2 3 4 kHz

Fig. 20. The sam as Fig. 19 but closed period increased by 1.3 ms, F1 ~ 2 . 5 Fo. Pulse flow enhanced, flow derivative reduced.

/0/, LIP PRESSIJRE FFT f i r s t pulse +6dB/oct

-

-

140 - t

110

-I M

1 Fig. 21 FFT of first period of ia I -1 4, Fig. 19. Radi-

ated sound pressure +6 1 , t --- I

1 - - - 1 - 1 dB/Oct extra emphasis. CI 1 2 3 4 kHz

', I

STL-QPSR 2-3/1985 - 41 - I

1 I I I I I I

0 1 3 3 f t kHz

Vowel [$I

Single period FFT. Hamming window

r - ~ r - ~ r . . . .

, . . - To = 6.7 ms

-

-

I I I 9 1 2 3 4 kHz

Fig. 22. Vowel d of Figs. 19 and 20, radiated sound pressure. 1st and 2nd period gated with Hamning win&.

I I

I Vowel /Bi

I FFT, Hamming window over period To

Fig. 23. Tne same as Fig. 22 but T0=8 m s . Ccmparison of first pulse response. TO=5. 4 ms and T0=8 ms.

1 dB I I 11 I I * I dB 1 1 1 6 0 - I I

150 - - - /Ist per iod - - -

. . . . 140 - -

-

130 - - . .. - -

120 - . -

i I I I I I I I I I 0 1 2 3 't kHz

-

i r) 1 2 3 't kHz

- To= 8 ms - -

160 m1-1-

- - 1st period

I -

F = 7 5 0 H z P=8crnH,O F0=714 B = 75 Hz Ago = 0 , l cm2 OQ = 0,64

ug'/ 1000 L = 5 , 0 m H T0'=1,4ms F, / Fo = 1,05 I I I I 1 I I I I I 1 I

,'- Pin . . , .

I . Fig. 26. Flow derivative and supraglottal pressure of i 1 conditions equal to those of Fig. 24. I

F = 750 Hz P = 8 cm H,O Fo = 476 B = 75 Hz Ago = 0,l crn2 0Q = 0,43

~ g ' / 1 0 0 0 L = 5,O mH TO= 2,l ms F,/ Fo = 1,58

I I r - - - i - - r - ~ Pin crn H,O

10

Fig. 27. Flaw derivative and supraglottal pressure otherwise as in Fig. 25.

apparent shifts in flow waveshape which may be described in terms of pulse skewing and overlayed ripple effects. This is one aspect of the superposition interaction. The waveshape exhibits changes from pulse to pulse accounting for a quasi-random perturbation which should notbe confused with random noise evoked through turbulent air streaming. The traditional terms jigger and shimmer do not suffice to catch these effects. One could widen the concept of shimmer from being a pure amplitude perturbation to incorporate waveshape and corresponding spec- tral variations. The relevance of this aperiodicity to naturalness of voice production remains to be assed. The study of Nord & al. (1984) was too limited in scope to provide a conclusive answer.

sbperposition ripple defined from the residual perturbations of the glottal-flow derivative waveshape after inverse filtering is not simply the matter of a residual first formant but appears to enhance a frequen- cy range of a little less than 2F1. On the other hand, in the complete sound the first formant is associated with a time-domain oscillation, the damping of which increases apparently in the glottal open phase. At a high pitch this damping is not sufficient to prevent superposition of formant energybut it modifies the extent of the fluctuations of overall formant amplitude at varying FO/~l ratio. Too much superposition has proved to be undesirable in speech synthesis. Cne aspect of the complex interaction from the F1 component of the supraglottal pressure is that F1 appears to condition the main pulse shape and thus the source spec- trum. These effects are most probable enhanced by the change in vocal- fold vibrational pattern induced by the supraglottal pressure and flow. These factors deserve a closer study.

Our study has shown that the viscosity component of glottal imped- ance adds somewhat to the interaction ripple and to creating a gradual onset of the flow pulse. At closure, the viscosity accounts for a similar shortening of the effective open phase but now with an enhance- ment of the flow derivative, as proposed by Rothenberg. However, in terms of formant excitation, this is a gain of no more than a couple of dB. In addition, the rounding-off of the flow termination adds a low- pass effect which is of minor importance. The glottal inductance has a similar effect as the viscosity in the opening phase but a reversed effect at closure. It tends to reduce the interaction ripple somewhat.

Our study of glottal leakage shows that a constant area added to an otherwise defined glottal area function does not change the rate of spectrum role-off. One effect of the leakage is the appearance of a true F1 oscillation in the maximally closed phase which should remain even after inverse filtering. The extra spectrum tilt observed with a leaky voice is due to a residual phase of slower rate of closure after the main discontinuity.

Acknawledgments Several of the studies reported in this article were originally

planned together with T.V. Ananthapadmanabha. The calculations per-

formed on the soprano voice were inspired by the papers of Rothenberg (1985) ard of Schutte & Miller (1985) for the Gotland Symposium on Voice Acoustics and Dysphonia, August 1985.

References Ananthapadmanabha, T.V. (1984): "Acoustic analysis of voice source dynamics", STGQPSR 2-3/1984, pp. 1-24.

Ananthapadmanabha, T.V. & Fant, G. (1982): "Calculation of true glot- tal flow and its components", STL-QPSR 1/1982, pp. 1-30; also in Speech Communication - 1 (1982), pp. 167-184.

Childers, D.G.1 Alsaka, Y., Hicks, D.M., & Moore, G.P. (1985) : "Vocal fold vibrations in dysphonia: EGG model and measurements", paper pre- sented at the Symposium on Voice Acoustics and Dysphonia, Gotland, Sweden, Aug.

Fant, G. (1982): "Preliminaries to analysis of the human voice source", STL-QPSR 4/1982, pp. 1-27.

Fant, G. & Anantl~apadmanabha, T.V. (1982): "Truncation and superposi- tion", STGQPSR 2-3/1982, pp 1-17.

Fant, Go, Lil jencrants, J., & Lin, Q-g. (1985): "A four-parameter model of glottal flow", paper presented at the French-Swedish Symposium, (:renoble, France, April.

Gob1 , C . ( forthcaning ) : Thesis wrk . Nord, L., Ananthapadmanabha, T.V.1 & Fant, G. (1985) : "Perceptual tests of vowel responses with an interactive source filter model and considerations for synthesis strategies", paper presented at the French- Swedish Symposium, Grenoble, France, April.

Rothenberg, M. (1981a): "An interactive model for the voice source", STGQPSR 4/1981, pp. 1-17.

Rothenberg, M. (1981b): "The voice source in singing", pp. 15-31 in Research Aspects in Singing, Royal Swedish Academy of Music, publ. 33, Stockholm.

Rothenberg, M. (1985): "CosS fan tutte and what it means", draft for discussion, Fourth Int.Voca1 Fold Physiology Conf.

Schutte, H.K. & Miller, D.G. (1985) : "The effect of FO/F~ coincidence in soprano high notes on pressure at the glottis", paper presented at the Gotland Symposium on Voice Acoustics and Dysphonia, August.