def test_compare_multisine_with_sine(time, freq, amp):
# Compare the result of a call of sine and a similar call of multi_sine
# with one-element lists of amplitudes and frequencies.
x = sine(time=time, amp=amp, freq=freq)
multi_x = multi_sine(time=time, amps=[amp], freqs=[freq])
# Check for minimal callability and that maximum amplitude at
# timestamps is below default.
assert_almost_equal(x, multi_x)
def multisine_testsignal():
# set amplitude values of multi-sine componentens (last parameter is number of components)
sine_amps = np.random.randint(1, 4, 10)
# set frequencies of multi-sine components
sine_freqs = np.linspace(100, 500, len(sine_amps)) * 2 * np.pi
# define time axis
dt = 0.0001
time = np.arange(0.0, 0.2, dt)
# measurement noise standard deviation (assume white noise)
sigma_noise = 0.001
# generate test signal
testsignal = multi_sine(time, sine_amps, sine_freqs, noise=sigma_noise)
return testsignal, sigma_noise
def multisine_testsignal(dt=0.0001):
""" Additional helper function to create test multi-sine signal
"""
# set amplitude values of multi-sine componentens (last parameter is number of components)
sine_amps = np.random.randint(1, 4, 10)
# set frequencies of multi-sine components
sine_freqs = np.linspace(100, 500, len(sine_amps)) * 2 * np.pi
# define time axis
time = np.arange(0.0, 0.2, dt)
time = time[:prevpow2(len(time))]
# measurement noise standard deviation (assume white noise)
sigma_noise = 0.001
# generate test signal
testsignal = multi_sine(time, sine_amps, sine_freqs, noise=sigma_noise)
return testsignal, sigma_noise
import numpy as np
import matplotlib.pyplot as plt
from PyDynamic.uncertainty.propagate_DFT import AmpPhase2Time, Time2AmpPhase, GUM_DFTfreq, Time2AmpPhase_multi
from PyDynamic.misc.testsignals import multi_sine
# set amplitude values of multi-sine componentens (last parameter is number of components)
sine_amps = np.random.randint(1, 4, 10)
# set frequencies of multi-sine components
sine_freqs = np.linspace(100, 500, len(sine_amps)) * 2 * np.pi
# define time axis
dt = 0.0001
time = np.arange(0.0, 0.2, dt)
# measurement noise standard deviation (assume white noise)
sigma_noise = 0.001
# generate test signal
testsignal = multi_sine(time, sine_amps, sine_freqs, noise=sigma_noise)
plt.figure(1, figsize=(12, 6))
plt.plot(time, testsignal)
plt.xlabel("time in s")
plt.ylabel("signal amplitude in a.u.")
# uncertainty propagation from time domain to frequency domain
A, P, UAP = Time2AmpPhase(testsignal, sigma_noise**2)
f = GUM_DFTfreq(len(time), dt)
plt.figure(2, figsize=(12, 6))
plt.errorbar(f, A, np.sqrt(np.diag(UAP)[:len(A)]), fmt=".-")
plt.xlabel("frequency in Hz")
plt.ylabel("DFT magnitude values in a.u.")
def __init__(self):
multi_sine_amps = np.random.randint(1, 4, 10)
multi_sine_freqs = np.linspace(100, 500, len(multi_sine_amps)) * 2 * np.pi
time_step = 0.0001
time = np.arange(start=0.0, stop=0.2, step=time_step)
measure_noise_std_sigma = 0.001
testsignal = multi_sine(
time, multi_sine_amps, multi_sine_freqs, noise=measure_noise_std_sigma
)
plt.figure(1, figsize=(12, 6))
plt.plot(time, testsignal)
plt.xlabel("time in s")
plt.ylabel("signal amplitude in a.u.")
# uncertainty propagation from time domain to frequency domain
A, P, UAP = Time2AmpPhase(testsignal, measure_noise_std_sigma ** 2)
f = GUM_DFTfreq(len(time), time_step)
plt.figure(2, figsize=(12, 6))
plt.errorbar(f, A, np.sqrt(np.diag(UAP)[: len(A)]), fmt=".-")
plt.xlabel("frequency in Hz")
plt.ylabel("DFT magnitude values in a.u.")
# uncertainty propagation from frequency domain to time domain
x, ux = AmpPhase2Time(A, P, UAP)
plt.figure(3, figsize=(12, 6))
plt.subplot(211)
plt.errorbar(
time,
x,
np.sqrt(np.diag(ux)),
fmt=".-",
label="after DFT and iDFT using amplitude and phase",
)
plt.plot(time, testsignal, label="original signal")
plt.xlabel("time in s")
plt.ylabel("signal amplitude in a.u.")
plt.legend()
plt.subplot(212)
plt.plot(
time,
np.sqrt(np.diag(ux)),
label="uncertainty after DFT and iDFT using amplitude and phase",
)
plt.plot(
time,
np.ones_like(time) * measure_noise_std_sigma,
label="original uncertainty",
)
plt.xlabel("time in s")
plt.ylabel("uncertainty in a.u.")
plt.legend()
# # apply the same method to several signals with one call
M = 10
testsignals = np.zeros((M, len(time)))
for m in range(M):
testsignals[m, :] = multi_sine(
time, multi_sine_amps, multi_sine_freqs, noise=measure_noise_std_sigma
)
# select those frequencies of the 10 % largest magnitude values
indices = np.argsort(A)[: len(A) // 10]
# propagate from time to frequency domain and select specified frequencies
A_multi, P_multi, UAP_multi = Time2AmpPhase_multi(
testsignals, np.ones(M) * measure_noise_std_sigma ** 2, selector=indices
)
plt.figure(4, figsize=(12, 6))
plt.subplot(211)
plt.plot(f[indices], A_multi.T, linestyle=":")
plt.subplot(212)
plt.plot(f[indices], P_multi.T, linestyle=":")