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