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test.py
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test.py
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# Copyright (C) 2021 Xiyuan Li
#
# 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 <https://www.gnu.org/licenses/>.
import numpy as np
import scipy
import matplotlib.pyplot as plt
from s import *
def test():
# Generate a quadratic chirp signal
dt = 0.001; t = 3
rate = int(1/dt)
ts = np.linspace(0, t, int(t/dt))
data = scipy.signal.chirp(ts, 10, t, 120, method='quadratic')
# Compute S Transform Spectrogram
spectrogram = sTransform(data, sample_rate=rate, frate=rate/len(data),
downsample=None, frange=[0,500])
plt.imshow(abs(spectrogram), origin='lower', aspect='auto')
plt.title('Original Spectrogram')
plt.colorbar()
plt.show()
# Quick Inverse of ts from S Transform
inverse_ts, inverse_tsFFT = inverseS(spectrogram)
# Magnitude Compensation:
# with the assumption that ts is real and only positive freqs are kept
inverse_ts_comp = inverse_ts*2
# Plot the original signal and the recovered, magnitude compensated signal
fig, axs = plt.subplots(2,1)
axs[0].plot(data)
axs[1].plot(inverse_ts_comp.real)
axs[0].set_title('Original Signal')
axs[1].set_title('(inverseS) Freq-passed, down-sampled Signal')
plt.show()
plt.plot(inverse_ts_comp)
plt.plot(inverse_ts_comp-data)
plt.title('Time Series Reconstruction Error')
plt.legend(['Recovered ts', 'Error'])
plt.show()
# Compute S Transform Spectrogram on the recovered time series
# however, information could be lost in the forward ST due to downsampling
# in both time and frequency
inverseSpectrogram = sTransform(inverse_ts,
sample_rate=len(inverse_ts)/len(data)*rate,
frange=[0,500])
plt.imshow(abs(inverseSpectrogram), origin='lower', aspect='auto')
plt.title('Recovered Spectrogram (inverseS)')
plt.colorbar()
plt.show()
return
if __name__ == '__main__':
test()