def test_time_to_freq_to_time(debug=False):
print("Test time -> freq -> time")
# Create time-domain data
t1 = np.arange(0, 20e-3, 1e-4)
x1 = _signal_model(t1)
# Frequency domain
f, X = czt.time2freq(t1, x1)
# Back to time domain
t2, x2 = czt.freq2time(f, X, t=t1)
# Plot for debugging purposes
if debug:
plt.figure()
plt.title("Imaginary")
plt.plot(t1, x1.imag, 'k', label='Original')
plt.plot(t2, x2.imag, 'r', label='Recovered')
plt.legend()
plt.figure()
plt.title("Real")
plt.plot(t1, x1.real, 'k', label='Original')
plt.plot(t2, x2.real, 'r', label='Recovered')
plt.legend()
plt.show()
# Compare
np.testing.assert_almost_equal(x1, x2, decimal=12)
def test_freq_to_time_convserions():
"""Test frequency <-> time domain conversions."""
# Time data
t1 = np.arange(0, 20e-3, 1e-4)
dt = t1[1] - t1[0]
Fs = 1 / dt
N = len(t1)
# Signal data
def model(t):
output = (1.0 * np.sin(2 * np.pi * 1e3 * t) +
0.3 * np.sin(2 * np.pi * 2e3 * t) +
0.1 * np.sin(2 * np.pi * 3e3 * t)) * np.exp(-1e3 * t)
return output
x1 = model(t1)
# Frequency domain
f, X = czt.time2freq(t1, x1)
# Back to time domain
t2, x2 = czt.freq2time(f, X)
# # Debug
# import matplotlib.pyplot as plt
# plt.figure()
# plt.plot(t1, x1.real)
# plt.plot(t2, x2.real)
# plt.show()
# Compare
np.testing.assert_almost_equal(x1, x2, decimal=12)
def test_time_zoom(debug=False):
print("Test time-domain zoom")
# Create time-domain data
t = np.arange(0, 20e-3 + 1e-10, 1e-4)
x = _signal_model(t)
dt = t[1] - t[0]
# Generate frequency-domain signal using DFT
f, X = czt.dft(t, x)
# Time domain
t1, x1 = czt.freq2time(f, X, t=t)
# Time domain: zoom
mask = (0.001 <= t1) & (t1 <= 0.002)
t2, x2 = czt.freq2time(f, X, t=t1[mask])
# Plot for debugging purposes
if debug:
plt.figure()
plt.title("Imaginary")
plt.plot(t, np.imag(x), 'k-', label='Original')
plt.plot(t1, np.imag(x1), 'ro:', label='freq2time: full')
plt.plot(t2, np.imag(x2), 'bv-', label='freq2time: zoom')
plt.xlim([0, 0.003])
plt.legend()
plt.figure()
plt.title("Real")
plt.plot(t, np.real(x), 'k-', label='Original')
plt.plot(t1, np.real(x1), 'ro:', label='freq2time: full')
plt.plot(t2, np.real(x2), 'bv-', label='freq2time: zoom')
plt.xlim([0, 0.003])
plt.legend()
plt.show()
# Compare
np.testing.assert_almost_equal(x, x1, decimal=12)
np.testing.assert_almost_equal(x[mask], x2, decimal=12)
def test_compare_czt_to_analytic_expression(debug=False):
print("Compare CZT to analytic expression")
# Create time-domain data
t = np.linspace(0, 50, 10001) * 1e-3
x = _signal_model(t)
# CZT
f, X_czt = czt.time2freq(t, x)
# Build frequency domain signal
X = _signal_model_f(f, len(t))
# Transform back to time-domain
_, x_iczt = czt.freq2time(f, X_czt, t=t)
# Truncate
mask = (0 < f) & (f < 5e3)
f, X, X_czt = f[mask], X[mask], X_czt[mask]
# Plot for debugging purposes
if debug:
plt.figure()
plt.title("Freq-Domain: Imaginary")
plt.plot(f / 1e3, X_czt.imag, label="CZT")
plt.plot(f / 1e3, X.imag, 'r--', label="Analytic")
plt.legend()
plt.figure()
plt.title("Freq-Domain: Real")
plt.plot(f / 1e3, X_czt.real, label="CZT")
plt.plot(f / 1e3, X.real, 'r--', label="Analytic")
plt.legend()
plt.figure()
plt.title("Freq-Domain: Absolute")
plt.plot(f / 1e3, np.abs(X_czt), label="CZT")
plt.plot(f / 1e3, np.abs(X), 'r--', label="Analytic")
plt.legend()
plt.show()
# Compare
np.testing.assert_allclose(X, X_czt, atol=0.1)
np.testing.assert_almost_equal(x, x_iczt, decimal=12)
def test_compare_iczt_idft(debug=False):
print("Compare ICZT and IDFT")
# Create time-domain signal
t = np.arange(0, 20e-3, 1e-4)
x = _signal_model(t)
# Frequency domain using DFT
f, X = czt.dft(t, x)
# Get time-domain using ICZT
_, x_iczt = czt.freq2time(f, X, t)
# Get time-domain using IDFT
_, x_idft = czt.idft(f, X, t)
# Plot for debugging purposes
if debug:
plt.figure()
plt.title("Imaginary")
plt.plot(t, x.imag, 'k', label="Original")
plt.plot(t, x_iczt.imag, 'g:', label="ICZT")
plt.plot(t, x_idft.imag, 'r--', label="IDFT")
plt.legend()
plt.figure()
plt.title("Real")
plt.plot(t, x.real, 'k', label="Original")
plt.plot(t, x_iczt.real, 'g:', label="ICZT")
plt.plot(t, x_idft.real, 'r--', label="IDFT")
plt.legend()
plt.figure()
plt.title("Real: error")
plt.plot(t, x_iczt.real - x.real, 'k', label="Original")
plt.show()
# Compare
np.testing.assert_almost_equal(x_iczt, x, decimal=12)
np.testing.assert_almost_equal(x_idft, x, decimal=12)
np.testing.assert_almost_equal(x_iczt, x_idft, decimal=12)