Figure 1.
Sketch of the Zebra finch vocal system (A).
Sounds are produced in the syringeal valves, and then filtered through the vocal tract. In the syrinx, the labia oscillate modulating the airflow. They support two coordinated modes of oscillation: an upward propagating superficial wave, and an oscillation around their mass centers (C). In the vocal tract we highlight trachea, glottis, OEC and beak. Pressure is the subsyringeal pressure,
stands for the pressure at the input of the tube and
stands for the pressure at the output of the trachea. In order to compute the model, we write the equivalent circuit of the post-tracheal part of the vocal tract (B).
Figure 2.
Sketch of the bifurcations found in the model of the syrinx leading to oscillatory solutions.
When parameter crosses a SNIC bifurcation, two fixed points collide within a limit cycle (A). The limit cycle is born with large period and rich spectral content, as sketched for the temporal series of the
variable and its corresponding spectrogram. When parameter
crosses a Hopf bifurcation, a stable fixed point loses stability against a newborn limit cycle (B). Close to the bifurcation, this limit cycle exhibits small period and ideally tonal spectral content, as sketched for the temporal series of the
variable and its corresponding spectrogram. Both bifurcations occur at distinct regions in the
parameter space [5], [28].
Figure 3.
Illustration of the parameter fitting and calibration procedure.
The thoracic air sac pressure is recorded together with the song; the pressure and corresponding sound of a bout are shown in (A). With these records, the temporal series that originate the syllables corresponding to the motif are constructed (B). After muting the bird and registering the pressure gesture as it attempts to produce a motif, the detection algorithm is tuned. In (C) we show the degraded pressure gesture, together with the correlation with the chosen segment of the intact pressure gesture. The segments pointed out by arrows indicate the detection of the intention to sing a motif. Song is synthesized during these periods by integration of the model with the parameters
found previously. In (D), we show the pressure gesture of the muted bird and the output of the trigger/integrate algorithm.
Figure 4.
Sketch of the experimental setup where the muted bird drives the electronic vocal organ.
The pressure gesture of the bird is recorded simultaneously with its song. Then, the parameters driving the normal form to produce synthetic song are reconstructed, and the bird is muted. The bird is then connected to the electronic syrinx via its thoracic air sac pressure, which is digitized and fed to the DSP. In the DSP, an algorithm detects the onset of the first syllable of the motif in the degraded gesture of the muted bird. Upon detection, the model is integrated in real-time while the attempt of the bird to continue with the motif is inferred from the motor gesture. The computed pressure fluctuations at the output of the beak are converted to an analog signal and played through a speaker located away from the bird.
Figure 5.
Intact song and subject-driven, synthetic song.
Intact pressure gesture and sonogram, with different colors and opacity of shading indicating the different syllables, and an arrow indicating the segment of the first syllable used for detection (upper panels). When the muted bird drives the syrinx, we see in the sonogram that synthetic sound is produced after the first syllable is detected and until recognition of the interruption of the motif (lower panels).