Biomedical Engineering Reference
In-Depth Information
(a)
(b)
k
F
4
4
3
3
5
2
1
(1)
2
(5)
p
T
Fig. 5.5.
If we enter the region of oscillations with a value of the parameter
k
similar to the value at which we exit the region, the syllable will have a fundamental
frequency that evolves in time like a “mountain”. In this case,
f
0
∼
0
parameter space). In this way, the syllable shows a time interval in which the
frequency decreases, like one of the syllables in Fig. 5.1.
Along the same lines of analysis, we can understand how it is possible to
generate a downsweep syllable. We should think of a path in the parameter
space similar to the one displayed in Fig. 5.4, but traversed in reverse order.
This means that the pressure should be delayed with respect to the tension,
as opposed to the case shown in Fig. 5.4. This can be done by choosing
φ
0
to have a value between zero and
π
. Before the oscillations start, the tension
value should be high, and only after such a tension level is reached does the
bronchial pressure increase to the value necessary for the oscillations to start.
After this, the tension decreases. Finally, the pressure will decrease to values
small enough that dissipation dominates the dynamics, and the labia will
stop. The tension should increase again, if we want the cycle to repeat itself.
That the most important morphological features of a syllable can be un-
derstood in such simple terms is remarkable. In Fig. 5.6 we show several dif-
ferent syllables, together with the paths in the parameter space that produced
them, and the corresponding phase differences. Every path was constructed
according to (5.8) and (5.9). The only difference between them is the choice
of the phase difference
φ
0
. Figure 5.6 says that the bronchial pressure and the
labial tension vary in a cyclic way, and by simply changing the relative delay
of a cycle with respect to the other we are able to change the morphology of a
syllable. Of course, there are many other changes that occur simultaneously
with this gesture: beak movements (which, as we saw, can modify the filtering
of the signal), posture, etc. However, the basic gesture necessary to produce
a syllable is a cycle in the bronchial pressure and the muscle tension.
