wavesongs.models.bird

Methods to implement the motor gesture model for birdsongs.

Functions

alpha_beta(obj[, z, method])
bifurcation_ode(f1, f2)
motor_gestures(obj, curves[, params])
set_params(obj[, params])
set_z(obj[, z])

wavesongs.models.bird._PARAMS = {'C': 343, 'Ch': 1.43e-10, 'L': 0.025, 'MB': 10000.0, 'MG': 20, 'RB': 5000000.0, 'Rh': 24000.0, 'gm': 40000.0, 'r': 0.65}

Model parameters

Birdsongs model parameters [A1].

Constant	Description	Value	Unit
\(\gamma\)	Time scaling constant	40000	\(dms\)
\(C\)	Speed of sound in media	343	\(m / s\)
\(L\)	Trachea length	0.025	\(m\)
\(r\)	Reflection coeficient	0.65	\(dms\)
\(Ch\)	OEC Compliance	1.43	\(m^3 / Pa\)
\(MG\)	Beak Inertance	20	\(kg / m^4\)
\(MB\)	Glottis Inertance	10000	\(kg / m^4\)
\(RB\)	Beak Resistance	5000000	\(s\; kg / m^4\)
\(Rh\)	OEC Resistence	24000	\(s\;kg / m^4\)

Where \(dms\) means dimensionless.

Type:

dict

wavesongs.models.bird._F1 = 'ys'

First linear equation. Where \(x\) is the labial position and \(y\) the labial wall velocity.

\[\frac{dx}{dt} = y\]

Type:

str

wavesongs.models.bird._F2 = '(-alpha-beta*xs-xs**3+xs**2)*gamma**2 - (xs+1)*gamma*xs*ys'

Second linear equation. Where \(x\) is the labial position and \(y\) the labial wall velocity.

\[\frac{dy}{dt} = \gamma^2(-\alpha-\beta x-x^3+x^2) - \gamma(x+1)x y\]

This equation is obtained using the Bogdanov–Takens bifurcation [A1].

Type:

str

wavesongs.models.bird._V_MAX_LABIA = -5000000.0

Maximum labia walls velocity.

Type:

float

wavesongs.models.bird._Z = {'a0': 0.11, 'b0': -0.1, 'b1': 1, 'b2': 0}

Motor gesture curves, air-sac pressure (\(\alpha\)) and labial wall tension (\(\beta\)). This function has two approaches:

(1)\[\begin{split}\begin{equation} \begin{aligned}[c] & \text{Performance}\\ \\ & \alpha(t) = a_0 \\ & \beta(t) = b_0 + b_1 \tilde{FF} + b_2 \tilde{FF}^2 \end{aligned} \qquad\qquad\qquad \begin{aligned}[c] & \text{Interpretability}\\ \\ & \alpha(t) = a_0 \\ & \beta(t) = b_0 + b_1 t + b_2 t^2 \end{aligned} \end{equation}\end{split}\]

The best performance, with the lowest relative errors, is obtained when the rescaled fundamental frequency is used as input through a quadratic composition, with \(\tilde{FF}=FF/10^4\).

Type:

dict

wavesongs.models.bird.bifurcation_ode(f1, f2)

Parameters:

• f1 (str)

• f2 (str)

Returns:

• beta_bif (np.array)

• mu1_curves (np.array)

• f1 (lambda functions)

• f2 (lambda functions)

Example

>>>

wavesongs.models.bird.alpha_beta(obj: Any, z: Dict = {'a0': 0.11, 'b0': -0.1, 'b1': 1, 'b2': 0}, method: Literal['best', 'fast'] = 'best') → List[array]

Parameters:

• obj (Song | Syllable)

• z (dict)

Returns:

• alpha (np.array([1,2…N])) – Bronchis pressure, also known as air-sac pressure.

• beta (np.array) – Labial tension.

Example

>>>

wavesongs.models.bird.motor_gestures(obj: Any, curves: List[array], params: Dict = {'C': 343, 'Ch': 1.43e-10, 'L': 0.025, 'MB': 10000.0, 'MG': 20, 'RB': 5000000.0, 'Rh': 24000.0, 'gm': 40000.0, 'r': 0.65}) → Syllable

Parameters:

pramams (Dict)

Returns:

synth – Synthethic syllable with same parameters except for s and vs

Return type:

Syllable

Example

>>>

wavesongs.models.bird.set_z(obj, z: List[float] | Dict = {'a0': 0.11, 'b0': -0.1, 'b1': 1, 'b2': 0}) → Dict

Parameters:

z (list[float] | dict) – [a0,a1,a2_,b,b1,b2,gamma]

Returns:

z

Return type:

dict

Exmaple

>>>

wavesongs.models.bird.set_params(obj, params: Tuple[float] | Dict = {'C': 343, 'Ch': 1.43e-10, 'L': 0.025, 'MB': 10000.0, 'MG': 20, 'RB': 5000000.0, 'Rh': 24000.0, 'gm': 40000.0, 'r': 0.65}) → Dict

Parameters:

params (list[float] | dict) – [a0,a1,a2_,b,b1,b2,gamma]

Returns:

params

Return type:

dict

Exmaple

>>>