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figure_anni_eq_illustration.py
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figure_anni_eq_illustration.py
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"""
figure_anni_eq_illustration.py: plot figure for annihilation equations
Copyright (C) 2017 Hanjie Pan
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
Correspondence concerning LEAP should be addressed as follows:
Email: hanjie [Dot] pan [At] epfl [Dot] ch
Postal address: EPFL-IC-LCAV
Station 14
1015 Lausanne
Switzerland
"""
from __future__ import division
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.patches as patches
if __name__ == '__main__':
tau = 1
alpha1 = 0.11
alpha2 = 0.2
alpha3 = 0.05
t1 = 0.15
t2 = 0.3
t3 = (t1 + t2) * 0.5 + 0.5 * tau
alpha_k = np.array([alpha1, alpha2, alpha3])
tk = np.array([t1, t2, t3])
# "continuous" time plot
t = np.linspace(0, tau, num=20000)
num_samples = 22
# t_samp = 0.1 + (0.55 - 0.1) * np.arange(num_samples) / num_samples
t_samp = np.arange(num_samples) / num_samples * tau
B = 9
m_grid, t_plt_grid = np.meshgrid(np.arange(-np.floor(B / 2.), 1 + np.floor(B / 2.)), t)
G = 1. / B * np.exp(2j * np.pi * m_grid * t_plt_grid)
tk_grid, m_grid_gt = np.meshgrid(tk, np.arange(-np.floor(B / 2.), 1 + np.floor(B / 2.)))
x_hat_noiseless = np.dot(np.exp(-2j * np.pi * m_grid_gt * tk_grid), alpha_k)
low_pass_sig = np.real(np.dot(G, x_hat_noiseless))
# sampling
m_grid, t_samp_grid = np.meshgrid(np.arange(-np.floor(B / 2.), 1 + np.floor(B / 2.)), t_samp)
G_samp = 1. / B * np.exp(2j * np.pi * m_grid * t_samp_grid)
low_pass_sig_samp = np.real(np.dot(G_samp, x_hat_noiseless))
# annihlating filter (in time)
Hz = lambda z: (1 - np.exp(-2j * np.pi / tau * t1) / z) * \
(1 - np.exp(-2j * np.pi / tau * t2) / z) * \
(1 - np.exp(-2j * np.pi / tau * t3) / z)
mask = Hz(np.exp(-2j * np.pi / tau * t))
filter_coef = np.zeros(3 + 1, dtype=complex)
filter_coef[0] = 1
filter_coef[1] = -np.exp(-2j * np.pi / tau * t1) - \
np.exp(-2j * np.pi / tau * t2) - \
np.exp(-2j * np.pi / tau * t3)
filter_coef[2] = np.exp(-2j * np.pi / tau * t1) * np.exp(-2j * np.pi / tau * t2) + \
np.exp(-2j * np.pi / tau * t1) * np.exp(-2j * np.pi / tau * t3) + \
np.exp(-2j * np.pi / tau * t2) * np.exp(-2j * np.pi / tau * t3)
filter_coef[3] = -np.exp(-2j * np.pi / tau * t1) * np.exp(-2j * np.pi / tau * t2) * \
np.exp(-2j * np.pi / tau * t3)
fig = plt.figure(figsize=(3.5, 1), dpi=90)
ax = fig.add_axes([0, 0.11, 1, 0.89])
markerline, stemlines, baseline = ax.stem(tk, alpha_k)
plt.setp(stemlines, linewidth=1, color=[0, 0.447, 0.741])
plt.setp(markerline, marker='', linewidth=1, markersize=8,
markerfacecolor='k', mec='k')
plt.setp(baseline, linewidth=0)
plt.axhline(0, color=[0.4, 0.4, 0.4], linewidth=0.5)
plt.xlim([0, tau])
ax.xaxis.set_label_coords(0.5, 0.02)
plt.tick_params(axis='both',
which='both',
bottom='off',
top='off',
left='off',
right='off',
labelbottom='off',
labelleft='off'
)
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
ax.spines['bottom'].set_visible(False)
ax.spines['left'].set_visible(False)
file_name = './result/AA_fig2a_sparse_conti.pdf'
plt.savefig(file_name, format='pdf', dpi=600, transparent=True)
fig = plt.figure(figsize=(3.5, 0.78), dpi=90)
ax = fig.add_axes([0, 0.11, 1, 0.89])
line = plt.plot(t, low_pass_sig)
markerline, stemlines, baseline = \
plt.stem(t_samp, low_pass_sig_samp)
plt.setp(stemlines, linewidth=0.5, color=[0.466, 0.674, 0.188])
plt.setp(markerline, marker='o', linewidth=0.5, markersize=2,
markerfacecolor=[0.466, 0.674, 0.188], mec=[0.466, 0.674, 0.188])
plt.setp(baseline, linewidth=0)
plt.axhline(0, color=[0.4, 0.4, 0.4], linewidth=0.5)
plt.xlim([0, tau])
plt.setp(line, linestyle='-', color=[0.8, 0.8, 0.8], linewidth=0.5)
plt.tick_params(axis='both',
which='both',
bottom='off',
top='off',
left='off',
right='off',
labelbottom='off',
labelleft='off'
)
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
ax.spines['bottom'].set_visible(False)
ax.spines['left'].set_visible(False)
file_name = './result/AA_fig2b_samp.pdf'
plt.savefig(file_name, format='pdf', dpi=600, transparent=True)
fig = plt.figure(figsize=(3.5, 0.78), dpi=90)
ax = fig.add_axes([0, 0.11, 1, 0.89])
line = plt.plot(t, np.abs(mask))
plt.axhline(0, color=[0.4, 0.4, 0.4], linewidth=0.5)
plt.xlim([0, tau])
plt.setp(line, linestyle='-', color=[0.85, 0.325, 0.098], linewidth=0.5)
plt.tick_params(axis='both',
which='both',
bottom='off',
top='off',
left='off',
right='off',
labelbottom='off',
labelleft='off'
)
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
ax.spines['bottom'].set_visible(False)
ax.spines['left'].set_visible(False)
zoom_in_factor = 6
x_lim = plt.gca().get_xlim()
y_lim = plt.gca().get_ylim()
ax.add_patch(
patches.Rectangle(
(x_lim[0], y_lim[0] / zoom_in_factor),
x_lim[1] - x_lim[0],
(y_lim[1] - y_lim[0]) / zoom_in_factor,
alpha=0.08,
facecolor='black',
edgecolor='None'
)
)
file_name = './result/AA_fig2c_mask.pdf'
plt.savefig(file_name, format='pdf', dpi=600, transparent=True)
fig = plt.figure(figsize=(3.5, 0.78 / 2), dpi=90)
ax = fig.add_axes([0, 0.11, 1, 0.89])
line = plt.plot(t, np.abs(mask))
plt.xlim([0, tau])
plt.axhline(0, color=[0.4, 0.4, 0.4], linewidth=0.5)
plt.ylim([y_lim[0] / zoom_in_factor, y_lim[1] / zoom_in_factor])
plt.setp(line, linestyle='-', color=[0.85, 0.325, 0.098], linewidth=0.5)
plt.tick_params(axis='both',
which='both',
bottom='off',
top='off',
left='off',
right='off',
labelbottom='off',
labelleft='off'
)
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
ax.spines['bottom'].set_visible(False)
ax.spines['left'].set_visible(False)
ax.add_patch(
patches.Rectangle(
(x_lim[0], y_lim[0] / zoom_in_factor),
x_lim[1] - x_lim[0],
(y_lim[1] - y_lim[0]) / zoom_in_factor,
alpha=0.08,
facecolor='black',
edgecolor='None'
)
)
file_name = './result/AA_fig2d_mask_zoom.pdf'
plt.savefig(file_name, format='pdf', dpi=600, transparent=True)
plt.show()