Time Frequency Transform for Chirp Signals
Step 1: Quadratic chirp signal
import numpy as np
import scipy
import matplotlib.pyplot as plt
# Generate a quadratic chirp signal
dt = 0.0001
rate = int(1/dt)
ts = np.linspace(0, 5, int(1/dt))
data = scipy.signal.chirp(ts, 10, 5, 300, method='quadratic')Step 2: S Transform Spectrogram
import TFchirp
# Compute S Transform Spectrogram
spectrogram = TFchirp.sTransform(data, sample_rate=rate)
plt.imshow(abs(spectrogram), origin='lower', aspect='auto')
plt.title('Original Spectrogram')
plt.show()
Step 3: Quick Recovery of ts from sTransform Spectrogram
# Quick ts Recovery from sTransform
inverse_ts = TFchirp.inverse_S(spectrogram)
plt.plot(inverse_ts-data)
plt.title('Time Series Reconstruction Error')
plt.show()
Recovered spectrogram:
# Compute S Transform Spectrogram on the recovered time series
inverseSpectrogram = TFchirp.sTransform(inverse_ts, sample_rate=rate)
plt.imshow(abs(inverseSpectrogram), origin='lower', aspect='auto')
plt.title('Recovered Specctrogram')
plt.show()
