def test_basic(self):
assert_allclose(windows.general_hamming(5, 0.7),
[0.4, 0.7, 1.0, 0.7, 0.4])
assert_allclose(
windows.general_hamming(5, 0.75, sym=False),
[0.5, 0.6727457514, 0.9522542486, 0.9522542486, 0.6727457514])
assert_allclose(
windows.general_hamming(6, 0.75, sym=True),
[0.5, 0.6727457514, 0.9522542486, 0.9522542486, 0.6727457514, 0.5])
def test_basic(self):
assert_allclose(windows.general_hamming(5, 0.7),
[0.4, 0.7, 1.0, 0.7, 0.4])
assert_allclose(windows.general_hamming(5, 0.75, sym=False),
[0.5, 0.6727457514, 0.9522542486,
0.9522542486, 0.6727457514])
assert_allclose(windows.general_hamming(6, 0.75, sym=True),
[0.5, 0.6727457514, 0.9522542486,
0.9522542486, 0.6727457514, 0.5])
def general_hamming(dataset, alpha, **kwargs):
r"""
Calculate generalized Hamming apodization.
For multidimensional NDDataset,
the apodization is by default performed on the last dimension.
The data in the last dimension MUST be time-domain or dimensionless,
otherwise an error is raised.
Functional form of apodization window :
.. math:: w(n) = \alpha - \left(1 - \alpha\right) \cos\left(\frac{2\pi{n}}{M-1}\right)
\qquad 0 \leq n \leq M-1
where M is the number of point of the input dataset.
Both the common Hamming window and Hann window are special cases of the
generalized Hamming window with :math:`\alpha` = 0.54 and :math:\alpha =
0.5, respectively
Parameters
----------
dataset : array.
Input dataset.
alpha : float
The window coefficient, :math:\alpha.
**kwargs
Optional keyword parameters (see Other Parameters).
Returns
-------
apodized
Dataset.
apod_arr
The apodization array only if 'retapod' is True.
Other Parameters
----------------
dim : str or int, keyword parameter, optional, default='x'
Specify on which dimension to apply the apodization method. If `dim` is specified as an integer it is equivalent
to the usual `axis` numpy parameter.
inv : bool, keyword parameter, optional, default=False
True for inverse apodization.
rev : bool, keyword parameter, optional, default=False
True to reverse the apodization before applying it to the data.
inplace : bool, keyword parameter, optional, default=False
True if we make the transform inplace. If False, the function return a new dataset.
retapod : bool, keyword parameter, optional, default=False
True to return the apodization array along with the apodized object.
See Also
--------
gm, sp, sine, sinm, qsin, hamming, triang, bartlett, blackmanharris
"""
x = dataset
return windows.general_hamming(len(x), alpha, sym=True)
# ***** # Filtering adapted to the signal # ***** # RANGE COMPRESSION if (hamming_rg): n_rg_eff = 2. * np.round((n_rg * B / f_s)/2.) h_hamming_rg_F = np.roll(np.concatenate((np.repeat(0., (n_rg - n_rg_eff) / 2.), general_hamming(int(n_rg_eff),hamming_rg_alpha), np.repeat(0., (n_rg - n_rg_eff) / 2.)),axis=0), int(n_rg / 2)) # Hamming window in range h_rg_desired = np.roll(np.less_equal(np.abs(t_rg-2*R0/c0), tau/2) *np.exp(- j* np.pi * B / tau * (t_rg - 2. * R0 / c0) ** 2.), int(n_rg / 2.)) # impulse response of the range compression filter temp_var=np.fft.fft(h_rg_desired)*np.conj(np.fft.fft(h_rg_desired)) for k in range(0, n_az): t_i_local=0 #t_i[k % len(t_i)] h_rg = np.roll(np.less_equal(np.abs(t_rg-2*R0/c0), tau/2) *np.exp((-1)**k*j * np.pi * B / tau * (t_rg - 2. * R0 / c0 - t_i_local - tau * np.floor((t_rg - 2. * R0 / c0 + tau / 2 - t_i_local) / tau)) ** 2.), int(n_rg / 2.)) h_rg_F_ideal=temp_var/np.fft.fft(h_rg)
# data [Rea199fc456d6-3]_. The facility uses various values for the :math:`\alpha` parameter
# based on operating mode of the SAR instrument. Some common :math:`\alpha`
# values include 0.75, 0.7 and 0.52 [Rea199fc456d6-4]_. As an example, we plot these different
# windows.
from scipy.signal.windows import general_hamming
from scipy.fftpack import fft, fftshift
import matplotlib.pyplot as plt
plt.figure()
plt.title("Generalized Hamming Windows")
plt.ylabel("Amplitude")
plt.xlabel("Sample")
spatial_plot = plt.axes()
plt.figure()
plt.title("Frequency Responses")
plt.ylabel("Normalized magnitude [dB]")
plt.xlabel("Normalized frequency [cycles per sample]")
freq_plot = plt.axes()
for alpha in [0.75, 0.7, 0.52]:
window = general_hamming(41, alpha)
spatial_plot.plot(window, label="{:.2f}".format(alpha))
A = fft(window, 2048) / (len(window) / 2.0)
freq = np.linspace(-0.5, 0.5, len(A))
response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
freq_plot.plot(freq, response, label="{:.2f}".format(alpha))
freq_plot.legend(loc="upper right")
spatial_plot.legend(loc="upper right")
# *****
# Filtering adapted to the signal
# *****
# RANGE COMPRESSION
if (hamming_rg):
n_rg_eff = 2. * np.round((n_rg * B / f_s) / 2.)
h_hamming_rg_F = np.roll(
np.concatenate((np.repeat(0., (n_rg - n_rg_eff) / 2.),
general_hamming(int(n_rg_eff), hamming_rg_alpha),
np.repeat(0., (n_rg - n_rg_eff) / 2.)),
axis=0), int(n_rg / 2))
# Hamming window in range
h_rg_desired = np.roll(
np.less_equal(np.abs(t_rg - 2 * R0 / c0), tau / 2) *
np.exp(-j * np.pi * B / tau * (t_rg - 2. * R0 / c0)**2.), int(n_rg / 2.))
# impulse response of the range compression filter
temp_var = np.fft.fft(h_rg_desired) * np.conj(np.fft.fft(h_rg_desired))
for k in range(1, n_az - 1):
t_i_local = 0 #t_i[k % len(t_i)]