cbadc.analog_system.modulator.SineWaveModulator
- class cbadc.analog_system.modulator.SineWaveModulator(analog_system: AnalogSystem, modulation_frequency: float)[source]
Bases:
AnalogSystemSinewave modulator
This class represents a sinewave modulator with a given modulation frequency and permutation matrix.
- Parameters
modulation_frequency (float) – the modulation frequency
permuation_matrix (array_like, shape=(N, N)) – the permutation matrix
Methods
__init__(analog_system, modulation_frequency)Create an analog system.
control_observation(t, x[, u, s])Computes the control observation for a given state vector \(\mathbf{x}(t)\) evaluated at time \(t\).
Evaluates the transfer functions between control signals and the system output.
demodulate(t)Downmodulate the given signal phi.
derivative(x, t, u, s)Compute the derivative of the analog system.
eta2(BW)Compute the eta2 parameter of the system.
Compute the symbolic homogenious solution
modulate(t)Upmodulate the given signal phi.
Computes the signal observation for a given state vector \(\mathbf{x}(t)\) evaluated at time \(t\).
symbolic_differential_equations(input, dim)Organise system matrixes into ordinary differential equations
transfer_function_matrix(omega[, symbolic, ...])Evaluate the analog signal transfer function at the angular frequencies of the omega array.
zpk([input])return zero-pole-gain representation of system
Attributes
pre_computable- control_observation(t: float, x: ndarray, u: ndarray = None, s: ndarray = None) ndarray[source]
Computes the control observation for a given state vector \(\mathbf{x}(t)\) evaluated at time \(t\).
Specifically, returns
\(\tilde{\mathbf{s}}(t) = \tilde{\mathbf{\Gamma}}^\mathsf{T} \mathbf{x}(t) + \tilde{\mathbf{D}} \mathbf{u}(t)\)
- Parameters
x (array_like, shape=(N,)) – the state vector.
u (array_like, shape=(L,)) – the input vector
s (array_like, shape=(M,)) – the control signal
- Returns
the control observation.
- Return type
array_like, shape=(M_tilde,)
- control_signal_transfer_function_matrix(omega: ndarray) ndarray
Evaluates the transfer functions between control signals and the system output.
Specifically, evaluates
\(\bar{\mathbf{G}}(\omega) = \mathbf{C}^\mathsf{T} \left(\mathbf{A} - i \omega \mathbf{I}_N\right)^{-1} \mathbf{\Gamma} \in \mathbb{R}^{\tilde{N} \times M}\)
for each angular frequency in omega where \(\mathbf{I}_N\) represents a square identity matrix of the same dimensions as \(\mathbf{A}\) and \(i=\sqrt{-1}\).
- Parameters
omega (array_like, shape=(K,)) – an array_like object containing the angular frequencies for evaluation.
- Returns
the signal transfer function evaluated at K different angular frequencies.
- Return type
array_like, shape=(N_tilde, M, K)
- derivative(x: ndarray, t: float, u: ndarray, s: ndarray) ndarray[source]
Compute the derivative of the analog system.
Specifically, produces the state derivative
\(\dot{\mathbf{x}}(t) = \mathbf{A} \mathbf{x}(t) + \mathbf{B} \mathbf{u}(t) + \mathbf{\Gamma} \mathbf{s}(t)\)
as a function of the state vector \(\mathbf{x}(t)\), the given time \(t\), the input signal value \(\mathbf{u}(t)\), and the control contribution value \(\mathbf{s}(t)\).
- Parameters
x (array_like, shape=(N,)) – the state vector evaluated at time t.
t (float) – the time t.
u (array_like, shape=(L,)) – the input signal vector evaluated at time t.
s (array_like, shape=(M,)) – the control contribution evaluated at time t.
- Returns
the derivative \(\dot{\mathbf{x}}(t)\).
- Return type
array_like, shape=(N,)
- eta2(BW)
Compute the eta2 parameter of the system.
- Parameters
BW (float) – bandwidth of the system
- Returns
eta2 parameter of the system at bandwidth BW
- Return type
float
- homogenius_solution()
Compute the symbolic homogenious solution
This is done by analytically computing the matrix exponential
\(\exp(\mathbf{A} t)\)
- Returns
the resulting matrix expression.
- Return type
sympy.Matrix
- signal_observation(x: ndarray) ndarray
Computes the signal observation for a given state vector \(\mathbf{x}(t)\) evaluated at time \(t\).
Specifically, returns
\(\mathbf{y}(t)=\mathbf{C}^\mathsf{T} \mathbf{x}(t)\)
- Parameters
x (array_like, shape=(N,)) – the state vector.
- Returns
the signal observation.
- Return type
array_like, shape=(N_tilde,)
- symbolic_differential_equations(input: Function, dim: int, input_signal=True)
Organise system matrixes into ordinary differential equations
- Parameters
input (
sympy.Matrix) – the input functiondim (int) – the dimension of the input
input_signal (bool) – determine if it is a input signal or digital control that is to be computed, defaults to True (input signal not control).
- Returns
[:py:class:`sympy:Eq] – the resulting symbolic system equations
[
sympy:Function] – the functions for which the equations relate.
- transfer_function_matrix(omega: ndarray, symbolic: bool = False, general=False) ndarray
Evaluate the analog signal transfer function at the angular frequencies of the omega array.
Specifically, evaluates
\(\mathbf{G}(\omega) = \mathbf{C}^\mathsf{T} \left(\mathbf{A} - i \omega \mathbf{I}_N\right)^{-1} \mathbf{B} + \mathbf{D}\)
for each angular frequency in omega where \(\mathbf{I}_N\) represents a square identity matrix of the same dimensions as \(\mathbf{A}\) and \(i=\sqrt{-1}\).
- Parameters
omega (array_like, shape=(K,)) – an array_like object containing the angular frequencies for evaluation.
symbolic (bool, optional) – solve using symbolic methods, defaults to True.
general (bool, optional) – to return general transfer function or not, defaults to False.
- Returns
the signal transfer function evaluated at K different angular frequencies.
- Return type
array_like, shape=(N_tilde, L, K)
- zpk(input=0)
return zero-pole-gain representation of system
- Parameters
input – determine for which input (in case of L > 1) to compute zpk, defaults to 0.
int – determine for which input (in case of L > 1) to compute zpk, defaults to 0.
optional – determine for which input (in case of L > 1) to compute zpk, defaults to 0.
- Returns
z,p,k the zeros, poles and gain of the system
- Return type
array_like, shape=(?, ?, 1)