def directional_response(self, theta, phi, polarization):
"""
Generate the (complex) frequency-dependent directional response.
For given angles and polarization direction, use the model of the
directional and polarization gains of the antenna to generate a
function for the interpolated response of the antenna with respect to
frequency. Used with the `frequency_response` method to calculate
effective heights.
Parameters
----------
theta : float
Polar angle (radians) from which a signal is arriving.
phi : float
Azimuthal angle (radians) from which a signal is arriving.
polarization : array_like
Normalized polarization vector in the antenna coordinate system.
Returns
-------
function
A function which returns complex-valued voltage gains for given
frequencies, using the values of incoming angle and polarization.
See Also
--------
ARAAntenna.frequency_response : Calculate the (complex) frequency
response of the antenna.
"""
e_theta = [
np.cos(theta) * np.cos(phi),
np.cos(theta) * np.sin(phi), -np.sin(theta)
]
e_phi = [-np.sin(phi), np.cos(phi), 0]
theta_factor = np.dot(polarization, e_theta)
phi_factor = np.dot(polarization, e_phi)
theta_gains = complex_bilinear_interp(x=np.degrees(theta),
y=np.degrees(phi),
xp=self._response_zens,
yp=self._response_azis,
fp=self._theta_response,
method='cartesian')
phi_gains = complex_bilinear_interp(x=np.degrees(theta),
y=np.degrees(phi),
xp=self._response_zens,
yp=self._response_azis,
fp=self._phi_response,
method='cartesian')
freq_interpolator = lambda frequencies: complex_interp(
x=frequencies,
xp=self._response_freqs,
fp=theta_factor * theta_gains + phi_factor * phi_gains,
method='euler',
outer=0)
return freq_interpolator
def test_euler_extrapolation(self):
"""Test euler complex extrapolation"""
steps = np.arange(5)
extrap_steps = [steps[0] - 1, steps[-1] + 1]
gain = np.array([1, 2, 3, 2, 1])
phase = np.radians([45, 90, 180, 90, 45])
extrap = complex_interp(extrap_steps,
steps,
gain * np.exp(1j * phase),
method='euler',
outer=None)
assert np.allclose(np.abs(extrap), [gain[0], gain[-1]])
assert np.allclose(np.angle(extrap), [phase[0], phase[-1]])
extrap2 = complex_interp(extrap_steps,
steps,
gain * np.exp(1j * phase),
method='euler',
outer=0)
assert np.array_equal(extrap2, [0, 0])
def test_cartesian_extrapolation(self):
"""Test cartesian complex extrapolation"""
steps = np.arange(5)
extrap_steps = [steps[0] - 1, steps[-1] + 1]
real = np.array([1, 2, 3, 2, 1])
imag = np.array([3, 2, 1, 2, 3])
extrap = complex_interp(extrap_steps,
steps,
real + 1j * imag,
method='cartesian',
outer=None)
assert np.array_equal(np.real(extrap), [real[0], real[-1]])
assert np.array_equal(np.imag(extrap), [imag[0], imag[-1]])
extrap2 = complex_interp(extrap_steps,
steps,
real + imag,
method='cartesian',
outer=0)
assert np.array_equal(extrap2, [0, 0])
def test_euler_phase_unwrapping(self):
"""Test phase unwrapping in euler complex interpolation"""
steps = np.arange(5)
interp_steps = steps[:-1] + 0.5
gain = np.array([1, 2, 3, 2, 1])
phase = np.radians([45, 90, 180, -90, -45])
interp = complex_interp(interp_steps,
steps,
gain * np.exp(1j * phase),
method='euler')
phase_interp = np.interp(interp_steps, steps, np.unwrap(phase))
phase_interp = phase_interp % (2 * np.pi)
phase_interp[phase_interp > np.pi] -= 2 * np.pi
assert np.allclose(np.angle(interp), phase_interp)
def test_euler_interpolation(self):
"""Test euler complex interpolation"""
steps = np.arange(5)
interp_steps = steps[:-1] + 0.5
gain = np.array([1, 2, 3, 2, 1])
phase = np.radians([45, 90, 180, 90, 45])
interp = complex_interp(interp_steps,
steps,
gain * np.exp(1j * phase),
method='euler')
gain_interp = np.interp(interp_steps, steps, gain)
phase_interp = np.interp(interp_steps, steps, phase)
assert np.allclose(np.abs(interp), gain_interp)
assert np.array_equal(np.angle(interp), phase_interp)
def test_cartesian_interpolation(self):
"""Test cartesian complex interpolation"""
steps = np.arange(5)
interp_steps = steps[:-1] + 0.5
real = np.array([1, 2, 3, 2, 1])
imag = np.array([3, 2, 1, 2, 3])
interp = complex_interp(interp_steps,
steps,
real + 1j * imag,
method='cartesian')
real_interp = np.interp(interp_steps, steps, real)
imag_interp = np.interp(interp_steps, steps, imag)
assert np.array_equal(np.real(interp), real_interp)
assert np.array_equal(np.imag(interp), imag_interp)
def interpolate_filter(self, frequencies):
"""
Generate interpolated filter values for given frequencies.
Calculate the interpolated values of the antenna's filter gain data
for some frequencies.
Parameters
----------
frequencies : array_like
1D array of frequencies (Hz) at which to calculate gains.
Returns
-------
array_like
Complex filter gain in voltage for the given `frequencies`.
"""
return complex_interp(x=frequencies,
xp=self._filter_freqs,
fp=self._filter_response,
method='euler',
outer=0)
