def atoms(n_points, coordinates):
"""Compute linear combination of elementary Gaussian atoms.
:param n_points: Number of points in a signal
:param coordinates: matrix of time-frequency centers
:type n_points: int
:type coordinates: array-like
:return: signal
:rtype: array-like
:Examples:
>>> coordinates = np.array([[32.0, 0.3, 32.0, 1.0],
[0.15, 0.15, 48.0, 1.22]])
>>> sig = atoms(128, coordinates)
>>> plot(real(sig))
.. plot:: docstring_plots/generators/misc/atoms.py
"""
if coordinates.ndim == 1:
coordinates = coordinates.reshape((coordinates.shape[0], 1))
signal = np.zeros((n_points,), dtype=complex)
n_atoms = coordinates.shape[0]
for k in range(n_atoms):
t0 = np.round(np.max((np.min((coordinates[k, 0], n_points)), 1)))
f0 = np.max((np.min((coordinates[k, 1], 0.5)), 0.0))
T = coordinates[k, 2]
A = coordinates[k, 3]
signal += A * amgauss(n_points, t0, T) * fmconst(n_points, f0, t0)[0]
return signal
def atoms(n_points, coordinates):
"""Compute linear combination of elementary Gaussian atoms.
:param n_points: Number of points in a signal
:param coordinates: matrix of time-frequency centers
:type n_points: int
:type coordinates: array-like
:return: signal
:rtype: array-like
:Examples:
>>> import numpy as np
>>> coordinates = np.array([[32.0, 0.3, 32.0, 1.0], [0.15, 0.15, 48.0, 1.22]])
>>> sig = atoms(128, coordinates)
>>> plot(real(sig)) #doctest: +SKIP
.. plot:: docstring_plots/generators/misc/atoms.py
"""
if coordinates.ndim == 1:
coordinates = coordinates.reshape((coordinates.shape[0], 1))
signal = np.zeros((n_points, ), dtype=complex)
n_atoms = coordinates.shape[0]
for k in range(n_atoms):
t0 = round(np.max((np.min((coordinates[k, 0], n_points)), 1)))
f0 = np.max((np.min((coordinates[k, 1], 0.5)), 0.0))
T = coordinates[k, 2]
A = coordinates[k, 3]
signal += A * amgauss(n_points, t0, T) * fmconst(n_points, f0, t0)[0]
return signal
def atoms(n_points, coordinates):
"""Compute linear combination of elementary Gaussian atoms.
:param n_points: Number of points in a signal
:param coordinates: matrix of time-frequency centers
:type n_points: int
:type coordinates: array-like
:return: signal
:rtype: array-like
:Examples:
>>> coordinates = np.array([[32.0, 0.3, 32.0, 1.0],
[0.15, 0.15, 48.0, 1.22]])
>>> sig = atoms(128, coordinates)
>>> plot(real(sig))
.. plot:: docstring_plots/generators/misc/atoms.py
"""
# FIXME: This function produces incorrect output when coordinates are
# one-dimensional.
signal = np.zeros((n_points,), dtype=complex)
n_atoms = coordinates.shape[0]
for k in xrange(n_atoms):
t0 = np.round(np.max((np.min((coordinates[k, 0], n_points)), 1)))
f0 = np.max((np.min((coordinates[k, 1], 0.5)), 0.0))
T = coordinates[k, 2]
A = coordinates[k, 3]
signal += A * amgauss(n_points, t0, T) * fmconst(n_points, f0, t0)[0]
return signal
def test_fmconst(self):
"""Test constant frequency modulation."""
n_points, fnorm, center = 129, 0.5, 64
signal, iflaw = fm.fmconst(n_points, fnorm, center)
real = np.real(signal)
np.testing.assert_allclose(iflaw.ravel(), fnorm * np.ones((n_points,)))
omega = np.arccos(real)[1:] / (2 * np.pi) / np.arange(n_points)[1:]
self.assertEqual(omega.max(), fnorm)
self.assert_is_analytic(signal)
def test_fmconst(self):
"""Test constant frequency modulation."""
n_points, fnorm, center = 129, 0.5, 64
signal, iflaw = fm.fmconst(n_points, fnorm, center)
real = np.real(signal)
np.testing.assert_allclose(iflaw.ravel(), fnorm * np.ones((n_points,)))
omega = np.arccos(real)[1:] / (2 * np.pi) / np.arange(n_points)[1:]
self.assertEqual(omega.max(), fnorm)
self.assert_is_analytic(signal)
def test_fmodany(self):
"""Test arbitrary modulation."""
iflaw = np.pad(np.ones((32,)), pad_width=(48, 48), mode='constant',
constant_values=0)
signal = fm.fmodany(iflaw / 2.0)
self.assert_is_analytic(signal)
np.testing.assert_allclose(np.real(signal)[:48],
np.ones((48,)))
np.testing.assert_allclose(np.real(signal)[-48:],
np.ones((48,)))
x = fm.fmconst(32, 0.5, 1)[0]
np.testing.assert_allclose(np.real(x), np.real(signal)[48:48 + 32])
def test_fmodany(self):
"""Test arbitrary modulation."""
iflaw = np.pad(np.ones((32,)), pad_width=(48, 48), mode='constant',
constant_values=0)
signal = fm.fmodany(iflaw / 2.0)
self.assert_is_analytic(signal)
np.testing.assert_allclose(np.real(signal)[:48],
np.ones((48,)))
np.testing.assert_allclose(np.real(signal)[-48:],
np.ones((48,)))
x = fm.fmconst(32, 0.5, 1)[0]
np.testing.assert_allclose(np.real(x), np.real(signal)[48:48 + 32])