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Anna Barney,
Antonio De StefanoISVR, University of Southampton, UK
&
Nathalie HenrichLAM, Université Paris VI, France
The Effect of Glottal Opening on the
Acoustic Response of the Vocal Tract
Introduction
We are interested in the interaction
between the voice source and the
vocal tract.
We hope that an improved
understanding of source-tract
interaction will enhance
naturalness in synthesised speech
Structure of this talk
• Types of source-tract interaction
• Effect of source-tract interaction on
formant frequencies: theory
• Mechanical model
• Measurement of the effect of source-
tract interaction: static
• Measurement of the effect of source-
tract interaction: dynamic
• Conclusions & Future work
Assumptions of Source-Filter Theory
• Source and vocal-tract filter do
not interact
• Non-linear effects are normally
lumped into the source model
• Formants are the resonances of
the vocal-tract, calculated when
the glottal impedance is infinite
Source Tract Interaction (STI)
Childers & Wong (1994) define 3 principal types of STI:
• Loading of the source by the vocal tract
impedance
• Dissipation of vocal tract energy by glottal
opening (mainly at F1)
• Carry over of energy from one glottal period to
the next (for low glottal damping)
(D.G. Childers and C.-F. Wong, 'Measuring and Modeling
Vocal Source-Tract Interaction', IEEE Transactions on
Biomedical Engineering, Vol. 41. No. 7. pp. 663-671
(1994) )
Source Tract Interaction (STI)
Flanagan (Speech analysis synthesis and
perception, 1965) considered the effect of
finite glottal impedance on a transmission
line model of the vocal tract
Za Za
Zb
Za Za
Zb
Zg
Zl
supraglottal vocal tract
Subglottal vocal tract
glottis
Zo
Source Tract Interaction (STI)
Flanagan stated that a finite glottal
impedance would raise F1 and
increase formant damping
He predicted and increase in F1 of
1.4% for a glottal area of 5 mm2
Source Tract Interaction (STI)
• Ananthapadmanabha, T.V. &
Fant G. (1982) (Calculation of the true glottal volume velocity and its
components. Speech Commun. 1 (1982) 167-184).
• Found the theoretical effect of
glottal inertance to be small
Source Tract Interaction (STI)
• P. Badin and G. Fant, (Notes on Vocal tract computation. STL-QPSR 2-3/1984 (1984) 53-108)
• Modelled the sub-glottal system as a short circuit
• used a glottal area of 0.027 mm2,
• glottis modelled by inductance only:
• F1 increased by 0.2%
Measurements on Real Speech
• It is known that the formant estimates vary depending on where in a pitch period the estimation window is placed.
• F1 estimated during open phase using group delay characteristics and a minimum phase assumption are generally a little higher during open phase than during closed phase.
(B Yeganarayana, R Veldhuis IEEE trans speech & audio processing, 6(4) 1998)
• Closed-phase formant analysis is used to get estimates of the vocal tract formants that are reliably decoupled from any sub-glottal formants.
(L.C.Wood, D.J.P Pearce IEE Proceedings 136 pt 1 no.2 1989)
Source Tract Interaction (STI)
Shifts in F1 may be small but they may
correlate with:
– changes in glottal OQ and/or
– changes in glottal amplitude
And may be of interest when considering
voice quality & naturalness of synthesis
Also – glottal areas considered in the
literature are always at the small end of
the range found in normal voicing.
Flanagan’s model
We implemented Flanagan’s
transmission line model with a
uniform duct of length
17.5 cm and area 2.89 cm2 to
explore the change as glottal width
increased
The formant shift – theory
Frequency (Hz)
Log
am
plit
ude
Theoretical modelling of the formant shift – static
glottis
To match our experimental measurements
we elaborated on Flanagan’s model
We used 4 T-sections for the supra-glottal
vocal tract and other parameters to
match those of our mechanical model
We chose the boundary condition at the
lips to match the boundary condition
for our measurements
Theoretical modelling of the formant shift –glottal
impedance model
Flanagan (1965) & others for
finite glottal impedance:
gg
g
gg
gg wh
lρωj
hw
lμZ
3
12
Theoretical modelling of–glottal impedance model
Laine & Karjalainen (1986):
where
gg
g
r
tg
ggg
A
dmddρL
A
AArUρ
hw
tμ
A
cρR
LωjRZ
4.0
169.01223
hw
ρωμ
πdmAdd
A
AA
g
t
gr
2
;48.0
Theoretical modelling of the formant shift –glottal
impedance model
Rösler & Strube (1989)
Where
kvidkgt LωjZRZ
2g
dkA
UρKR
gg
g
gg
gvi wh
lρωj
hw
lμZ
5
6123
;ln2
ω
D
αh
ρLk
Theoretical modelling of the formant shift –glottal
impedance model
• How should we model the sub-glottal impedance?
• Speech models often assume that the lower end of the trachea is a fully absorbing boundary (r=0) so that there are no sub-glottal resonances.
Theoretical modelling of the formant shift –glottal
impedance model
• We wanted to compare our theoretical model with measurements. We tried all three glottal impedance models and a range of sub-glottal impedance models to find the best fit to the data.
The Mechanical Model
We made our measurements of
F1 shift using a mechanical
model of the larynx and vocal
tract
Shutter Driver System
The shutter region
Schematic Diagram of the Model
115 175
17
pt1 pt2 pt 315
50 130 55
flow
All dimensions in mm, not to scale
Instrumentation Rotameter -Inlet volume flow rate
Manometer -Mean pressure upstream
Entran EPE-54 miniature pressure transducers, diameter of 2.36 mm, range 0 to 14kPa -Time-varying pressure at the duct wall for up to 4 locations.
Shutter driving signal - shutter position
All time-histories are captured by a simultaneous-sampling ADC connected to a PC with a sampling frequency of 8928 Hz.
Experimental measurements – static case
• Glottal widths of 0,1,2,3 mm
• Excitation provided by speaker at duct
outlet – tonal discrete frequencies
between 300 Hz and
2 kHz
• Speaker modified duct boundary
condition at “lips” so it was closer to a
closed end condition. Impedance here
was held constant throughout the
measurements
Experimental measurements – static case
• 2 pressure transducers between
“glottis” and “lips”
• Pressure transducer separation 80 mm
• Standing wave component pressure
amplitudes extracted as specified by
K R Holland & POAL Davies(The measurement of sound power flux in flow ducts. Journal of
Sound and Vibration 230 (2000) 915 - 932 )
• Transfer function from “glottis” to
“lips” obtained.
Transfer function from glottis to lips – measured &
theoretical - static
dB
Transfer function from glottis to lips – measured &
theoretical - static
dB
Transfer function from glottis to lips – measured &
theoretical - static
dB
Transfer function from glottis to lips – measured &
theoretical - static
dB
lZ
tA
cρ9.0
lZ lZ
tA
cρ98.19
lZ
lZ lZ
π1.0
lZ
π5.0
lZ
lZ lZtA
cρ6.0lZ
tA
cρ98.19
lZtA
cρ4.0
π3.0 lZ
π5.0π5.0 π1.0
tA
cρ2.1
tA
cρ2.1
tA
cρ8.0
tA
cρ7.0
tA
cρ9.0lZlZlZ
tA
cρ98.19lZ
tA
cρ3.0
lZ π5.0 lZ
π2.0 π00.0 lZ lZ lZπ5.0 lZ π1.0
lZ
π5.0
Glottal width
Flanagan model,
Flanagan factor of
6/5
L & K model
R & Smodel
1 mm
MSE 4.00 3.35 10.77 2.33
2 mm
MSE 7.95 7.26 16.81 5.86
3 mm
MSE 12.44 12.76 25.50 8.99
dB
0 mm
1 mm
2 mm
3 mm
Static case - Summary
• F1 & F2 increased with increasing glottal width
Predicted values of F1 (799 Hz, 854 Hz, 882
Hz, 896 Hz) match well to measurements
• Increase in F1 between closed glottis and 1 mm
wide glottis is ~6%
• Increase in F1 between closed glottis and 3 mm
wide glottis is ~13%
• Increase in F1 larger than found by previous
researchers, perhaps due to using greater glottal
widths
Dynamic Experimental measurements
• How do our measurements for the
static case transfer to a model
excited by a vibrating larynx?
• What is the dependence of F1 on
the open quotient?
• What is the dependence of F1 on
the glottal amplitude?
Experimental measurements – dynamic
• Moving shutters 10 – 40 Hz
square wave excitation
• OQ: 20, 40, 60, 80 %
• Glottal width: 0.25 mm to
4 mm
Peak glottal width versus OQ for all f0
20 40 60 80
Open quotient
G
lott
al a
mpl
itud
e
Pressure time history at p1 in the duct
Time (s)
Pre
ssur
e (P
a)
closure
opening
Experimental measurements – dynamic
• F1 frequency found from AR
spectral estimation. AR analysis
uses whole glottal cycle to ensure
STI effects included in analysis
• AR analysis uses the Yule-Walker
algorithm with an order of
ceil((Fs/1000)+2) = 11
Experimental measurements – dynamic
• F1 peak defined as maximum
value of spectrum between
200 Hz and 1 kHz
• Data set rejected if no peak visible
in this range hence small data set
for OQ = 80%
Frequency of F1 for changing glottal width and
OQ
Glottal width (mm)
F1
(Hz)
Summary – dynamic measurements
• F1 increases with increasing
glottal width for fixed OQ
• F1 increases with increasing OQ
for fixed glottal width – at least at
small glottal widths• Observed values of F1 much
higher than normally predicted for open-closed tube of the same length or expected for real speech.
Theoretical model – dynamic
• Simulink model
• Model adapted from one created
by Nicolas Montgermont and
Benoit Fabre, LAM for
investigating the flute
Duct modelSwitchable
glottal impedance
Glottal excitation
Simulink model of dynamic case
Pressure time history at P1 - simulated
openclosed
F1 values for dynamic simulation
Simulation - summary
• The simulation does show a change in the formant frequency as OQ changes
• The increase in F1 is much smaller than observed in the dynamic model experiments
• The dynamic model has much greater damping, especially during closure, than the simulation
Future work
• To make a theoretical model of the formant shift in the dynamic case that matches the measurements more closely
• To make similar measurements in real speakers
