def test_amgauss(self):
"""Test if the gaussian amplitude modulator works correctly."""
time_center = 63
n_points = 128
spread = 10
signal = am.amgauss(n_points, time_center, spread)
# parameters of the underlying gaussian function of the form
# f(x) = a * exp( (-(x - b) **2) / (2 * (c ** 2)))
a, b, c = 1, time_center, spread / np.sqrt(2 * pi)
# Integral of a Gaussian is a * c * sqrt( 2 * pi)
integral = a * c * np.sqrt(2 * pi)
self.assertAlmostEqual(integral, signal.sum())
# Other miscellaneous properties of a Gaussian
maximum = argrelmax(signal)
self.assertEqual(len(maximum), 1)
self.assertEqual(maximum[0][0], time_center - 1)
self.assertAlmostEqual(signal[time_center - 1], 1.0)
self.assert_is_monotonic_increasing(signal[:(time_center - 1)])
self.assert_is_monotonic_decreasing(signal[(time_center - 1):])
infpl1 = np.floor(b - c).astype(int) - 1
infpl2 = np.floor(b + c).astype(int)
self.assert_is_convex(signal[:infpl1])
self.assert_is_concave(signal[infpl1:infpl2])
self.assert_is_convex(signal[infpl2:])
def test_group_delay(self):
"""Test Group delay calculation."""
n_points = 128
signal = am.amgauss(n_points, 64, 30) * fm.fmlin(n_points, 0.1, 0.4)[0]
fnorm = np.arange(0.1, 0.38, step=0.04)
grp_dlay = fproc.group_delay(signal, fnorm)
self.assert_is_linear(grp_dlay, 0)
def test_amgauss(self):
"""Test if the gaussian amplitude modulator works correctly."""
time_center = 63
n_points = 128
spread = 10
signal = am.amgauss(n_points, time_center, spread)
# parameters of the underlying gaussian function of the form
# f(x) = a * exp( (-(x - b) **2) / (2 * (c ** 2)))
a, b, c = 1, time_center, spread / np.sqrt(2 * pi)
# Integral of a Gaussian is a * c * sqrt( 2 * pi)
integral = a * c * np.sqrt(2 * pi)
self.assertAlmostEqual(integral, signal.sum())
# Other miscellaneous properties of a Gaussian
maximum = argrelmax(signal)
self.assertEqual(len(maximum), 1)
self.assertEqual(maximum[0][0], time_center - 1)
self.assertAlmostEqual(signal[time_center - 1], 1.0)
self.assert_is_monotonic_increasing(signal[:(time_center - 1)])
self.assert_is_monotonic_decreasing(signal[(time_center - 1):])
infpl1 = np.floor(b - c).astype(int) - 1
infpl2 = np.floor(b + c).astype(int)
self.assert_is_convex(signal[:infpl1])
self.assert_is_concave(signal[infpl1:infpl2])
self.assert_is_convex(signal[infpl2:])
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_group_delay(self):
"""Test Group delay calculation."""
n_points = 128
signal = am.amgauss(n_points, 64, 30) * fm.fmlin(n_points, 0.1, 0.4)[0]
fnorm = np.arange(0.1, 0.38, step=0.04)
grp_dlay = fproc.group_delay(signal, fnorm)
self.assert_is_linear(grp_dlay, 0)
def test_loctime(self):
signal = am.amgauss(160, 80, 50)
tm, T = tmd.loctime(signal)
self.assertAlmostEqual(tm, 79, places=6)
self.assertAlmostEqual(T, 50, places=4)
def test_loctime(self):
"""Test computation of localized time characteristics."""
signal = am.amgauss(160, 80, 50)
tm, T = tmd.loctime(signal)
self.assertAlmostEqual(tm, 79, places=6)
self.assertAlmostEqual(T, 50, places=4)
def test_loctime(self):
"""Test computation of localized time characteristics."""
signal = am.amgauss(160, 80, 50)
tm, T = tmd.loctime(signal)
self.assertAlmostEqual(tm, 79, places=6)
self.assertAlmostEqual(T, 50, places=4)
