"""
Sample spectral profiles for signal injection.
For any given time sample,
these functions map out the intensity in the frequency direction (centered at
a particular frequency).
"""
import numpy as np
from astropy import units as u
from setigen import unit_utils
from setigen.funcs import func_utils
[docs]def box_f_profile(width):
"""
Square intensity profile in the frequency direction.
"""
width = unit_utils.get_value(width, u.Hz)
def f_profile(f, f_center):
return (np.abs(f - f_center) < width / 2).astype(int)
return f_profile
[docs]def gaussian_f_profile(width):
"""
Gaussian profile; width is the FWHM of the profile.
"""
width = unit_utils.get_value(width, u.Hz)
factor = 2 * np.sqrt(2 * np.log(2))
sigma = width / factor
def f_profile(f, f_center):
return func_utils.gaussian(f, f_center, sigma)
return f_profile
[docs]def multiple_gaussian_f_profile(width):
"""
Example adding multiple Gaussians in the frequency direction.
"""
width = unit_utils.get_value(width, u.Hz)
factor = 2 * np.sqrt(2 * np.log(2))
sigma = width / factor
def f_profile(f, f_center):
# Offsets by 100 Hz @ a quarter intensity, absolutely arbitrarily
return func_utils.gaussian(f, f_center - 100, sigma) / 4 \
+ func_utils.gaussian(f, f_center, sigma) \
+ func_utils.gaussian(f, f_center + 100, sigma) / 4
return f_profile
[docs]def lorentzian_f_profile(width):
"""
Lorentzian profile; width is the FWHM of the profile.
"""
width = unit_utils.get_value(width, u.Hz)
gamma = width / 2
def f_profile(f, f_center):
return func_utils.lorentzian(f, f_center, gamma)
return f_profile
[docs]def voigt_f_profile(g_width, l_width):
"""
Voigt profile; g_width and l_width are the FWHMs of the Gaussian and Lorentzian profiles.
Further information here: https://en.wikipedia.org/wiki/Voigt_profile.
"""
g_width = unit_utils.get_value(g_width, u.Hz)
factor = 2 * np.sqrt(2 * np.log(2))
sigma = g_width / factor
l_width = unit_utils.get_value(l_width, u.Hz)
gamma = l_width / 2
def f_profile(f, f_center):
return func_utils.voigt(f, f_center, sigma, gamma) / func_utils.voigt(f_center, f_center, sigma, gamma)
return f_profile
[docs]def sinc2_f_profile(width, trunc=True):
"""
Sinc squared profile; width is the FWHM of the squared normalized sinc function.
The trunc parameter controls whether or not the sinc squared profile is
truncated at the first root (e.g. zeroed out for more distant frequencies).
"""
width = unit_utils.get_value(width, u.Hz)
# Using the numerical solution for the FWHM
zero_crossing = (width / 2) / 0.442946470689452
def f_profile(f, f_center):
if trunc:
return np.where(np.abs(f - f_center) < zero_crossing,
np.sinc((f - f_center) / zero_crossing),
0)**2
else:
return np.sinc((f - f_center) / zero_crossing)**2
return f_profile