Signal#

class Signal(envelope, carrier_freq=0.0, phase=0.0, name=None)[source]#

Bases: object

General signal class.

Represents a function of the form:

\[Re[f(t)e^{i (2 \pi \nu t + \phi)}] = Re[f(t)]\cos(2 \pi \nu t + \phi) - Im[f(t)]\sin(2 \pi \nu t + \phi),\]

where

  • \(f(t)\) is the envelope function.

  • \(\nu\) is the carrier frequency.

  • \(\phi\) is the phase.

The envelope function can be specified either as a constant numeric value (indicating a constant function), or as a complex-valued callable, and the frequency and phase must be real.

Note

Signal assumes the envelope f is array vectorized in the sense that f can operate on arrays of arbitrary shape and satisfy f(x)[idx] == f(x[idx]) for a multidimensional index idx. This can be ensured either by writing f to be vectorized, or by using the vectorize function in numpy or jax.numpy.

For example, for an unvectorized envelope function f:

import numpy as np
vectorized_f = np.vectorize(f)
signal = Signal(envelope=vectorized_f, carrier_freq=2.)

Initializes a signal given by an envelope and a carrier.

Parameters:

  • envelope (Union[Callable, ndarray, number, int, float, complex, Tracer, Array, Array, spmatrix, BCOO, list]) – Envelope function of the signal, must be vectorized.

  • carrier_freq (Union[ndarray, number, int, float, complex, Tracer, Array, Array, spmatrix, BCOO, list]) – Frequency of the carrier. Subclasses such as SignalSums represent the carriers of each signal in an array.

  • phase (Union[ndarray, number, int, float, complex, Tracer, Array, Array, spmatrix, BCOO, list]) – The phase of the carrier. Subclasses such as SignalSums represent the phase of each signal in an array.

  • name (Optional[str]) – Name of the signal.

Methods

complex_value(t)[source]#

Vectorized evaluation of the complex value at time t.

Return type:

Union[ndarray, number, int, float, complex, Tracer, Array, Array, spmatrix, BCOO, list]

conjugate()[source]#

Return a new signal whose complex value is the complex conjugate of this one.

draw(t0, tf, n, function='signal', axis=None, title=None)[source]#

Plot the signal over an interval.

The function arg specifies which function to plot:

  • function == 'signal' plots the full signal.

  • function == 'envelope' plots the complex envelope.

  • function == 'complex_value' plots the complex_value.

Parameters:

  • t0 (float) – Initial time.

  • tf (float) – Final time.

  • n (int) – Number of points to sample in interval.

  • function (Optional[str]) – Which function to plot.

  • axis (Optional[axis]) – The axis to use for plotting.

  • title (Optional[str]) – Title of plot.

envelope(t)[source]#

Vectorized evaluation of the envelope at time t.

Return type:

Union[ndarray, number, int, float, complex, Tracer, Array, Array, spmatrix, BCOO, list]

Attributes

carrier_freq#

The carrier frequency of the signal.

is_constant#

Whether or not the signal is constant.

name#

Return the name of the signal.

phase#

The phase of the signal.