def gdpower(n_points, degree=0, rate=1):
"""Generate a signal with a power law group delay.
:param n_points: Number of points in time.
:param degree: degree of the power law.
:param rate: rate-coefficient of the power law GD.
:type n_points: int
:type degree: int
:type rate: float
:return: Tuple of time row containing modulated samples, group delay, \
frequency bins.
:rtype: tuple
"""
t0 = 0
lnu = np.round(n_points / 2)
nu = np.linspace(0, 0.5, lnu + 1)
nu = nu[1:]
am = nu ** ((degree - 2) / 6)
if rate == 0:
raise TypeError("rate must be non-zero")
tfx = np.zeros((n_points,), dtype=complex)
if (degree < 1) and (degree != 0):
d = n_points ** (degree * rate)
t0 = n_points / 10.0
tfx[:lnu] = np.exp(-1j * 2 * pi * (t0 * nu + d * nu ** degree / degree)) * am
x = np.fft.ifft(tfx)
elif degree == 0:
d = rate
t0 = n_points / 10.0
tfx[:lnu] = np.exp(-1j * 2 * np.pi * (t0 * nu + d * np.log(nu))) * am
x = np.fft.ifft(tfx)
elif degree == 1:
from analytic_signals import anapulse
t0 = n_points
x = anapulse(n_points, t0)
elif degree > 1:
d = n_points * 2 ** (degree - 1) * rate
tfx[:lnu] = np.exp(-1j * 2 * pi * (t0 * nu + d * nu ** degree / degree)) * am
x = np.fft.ifft(tfx)
else:
t0 = n_points / 10
d = n_points * 2 ** (degree - 1) * rate
tfx[:lnu] = np.exp(-1j * 2 * pi * (t0 * nu + d * np.log(nu))) * am
x = np.fft.ifft(tfx)
if degree != 1:
gpd = t0 + np.abs(np.sign(rate) - 1) / 2 * (n_points + 1) + d * nu ** (degree - 1)
else:
gpd = t0 * np.ones((n_points / 2,))
x = x - x.mean()
x = x / np.linalg.norm(x)
return x, gpd, nu
def gdpower(n_points, degree=0.0, rate=1.0):
"""Generate a signal with a power law group delay.
:param n_points: Number of points in time.
:param degree: degree of the power law.
:param rate: rate-coefficient of the power law GD.
:type n_points: int
:type degree: int # yoder: i'm pretty sure this is supposed to be a float. at least in test_misc.py, the test for this funct. passes degree=0.5
:type rate: float
:return: Tuple of time row containing modulated samples, group delay, \
frequency bins.
:rtype: tuple
"""
n_points = int(n_points)
degree = float(degree)
rate = float(rate)
t0 = 0
lnu = int(np.ceil(n_points / 2))
nu = np.linspace(0, 0.5, lnu + 1)
nu = nu[1:]
am = nu ** ((degree - 2.0) / 6.0)
if rate == 0.0:
raise TypeError("rate must be non-zero")
tfx = np.zeros((n_points,), dtype=complex)
if (degree < 1.0) and (degree != 0):
d = float(n_points) ** (degree * rate)
t0 = n_points / 10.0
tfx[:lnu] = np.exp(-1.0j * 2.0 * pi * (t0 * nu + d * nu ** degree / degree)) * am
x = np.fft.ifft(tfx)
elif degree == 0:
d = rate
t0 = n_points / 10.0
tfx[:lnu] = np.exp(-1j * 2 * np.pi * (t0 * nu + d * np.log(nu))) * am
x = np.fft.ifft(tfx)
elif degree == 1.0:
from analytic_signals import anapulse
t0 = n_points
x = anapulse(n_points, t0)
elif degree > 1.0:
d = n_points * 2.0 ** (degree - 1.0) * rate
tfx[:lnu] = np.exp(-1.0j * 2.0 * pi * (t0 * nu + d * nu ** degree / degree)) * am
x = np.fft.ifft(tfx)
else:
t0 = n_points / 10
d = n_points * 2.0 ** (degree - 1.0) * rate
tfx[:lnu] = np.exp(-1j * 2 * pi * (t0 * nu + d * np.log(nu))) * am
x = np.fft.ifft(tfx)
if degree != 1.0:
gpd = t0 + np.abs(np.sign(rate) - 1.0) / 2.0 * (n_points + 1.0) + d * nu ** (degree - 1.0)
else:
gpd = t0 * np.ones((n_points / 2.0,))
x = x - x.mean()
x = x / np.linalg.norm(x)
return x, gpd, nu
