def noisegen():
return at.Noise()
# (a=-4 random run FM)
if b == 0:
return pow(af, -1)
elif b == -1:
# f_h = 0.5/tau0 (assumed!)
# af = tau/tau0
# so f_h*tau = 0.5/tau0 * af*tau0 = 0.5*af
avar = (1.038 + 3 * np.log(2 * np.pi * 0.5 * af)) / (4.0 *
pow(np.pi, 2))
mvar = 3 * np.log(256.0 / 27.0) / (8.0 * pow(np.pi, 2))
return mvar / avar
else:
return pow(af, 0)
ng = at.Noise()
nr = pow(2, 14)
qd = 2e-20
b = -1
def remove_duplicates(l):
s = []
for i in l:
if i not in s:
s.append(i)
return s
plt.figure(figsize=(12, 10))
# N_points = pow(2,6)
def main():
nr = 2**14 # number of datapoints in time-series
adev0 = 1.0e-11
#
# for each noise type generated Noise class
# compute
# - phase PSD and coefficient g_b
# - frequency PSD and coefficient h_a
# - ADEV
# - MDEV
#
# discrete variance for noiseGen()
qd0 = qd1 = qd2 = qd3 = qd4 = pow(adev0, 2)
tau0 = 1.0 # sample interval
sample_rate = 1.0 / tau0
x0 = at.Noise(nr, qd0, 0) # white phase noise (WPM)
x0.generateNoise()
x1 = at.Noise(nr, qd1, -1) # flicker phase noise (FPM)
x1.generateNoise()
x2 = at.Noise(nr, qd2, -2) # white frequency noise (WFM)
x2.generateNoise()
x3 = at.Noise(nr, qd3, -3) # flicker frequency noise (FFM)
x3.generateNoise()
x4 = at.Noise(nr, qd4, -4) # random walk frequency noise (RWFM)
x4.generateNoise()
# compute frequency time-series
y0 = at.phase2frequency(x0.time_series, sample_rate)
y1 = at.phase2frequency(x1.time_series, sample_rate)
y2 = at.phase2frequency(x2.time_series, sample_rate)
y3 = at.phase2frequency(x3.time_series, sample_rate)
y4 = at.phase2frequency(x4.time_series, sample_rate)
# compute phase PSD
(f0, psd0) = at.noise.scipy_psd(x0.time_series,
f_sample=sample_rate,
nr_segments=4)
(f1, psd1) = at.noise.scipy_psd(x1.time_series,
f_sample=sample_rate,
nr_segments=4)
(f2, psd2) = at.noise.scipy_psd(x2.time_series,
f_sample=sample_rate,
nr_segments=4)
(f3, psd3) = at.noise.scipy_psd(x3.time_series,
f_sample=sample_rate,
nr_segments=4)
(f4, psd4) = at.noise.scipy_psd(x4.time_series,
f_sample=sample_rate,
nr_segments=4)
# compute phase PSD prefactor g_b
g0 = x0.phase_psd_from_qd(tau0)
g1 = x1.phase_psd_from_qd(tau0)
g2 = x2.phase_psd_from_qd(tau0)
g3 = x3.phase_psd_from_qd(tau0)
g4 = x4.phase_psd_from_qd(tau0)
# compute frequency PSD
(ff0, fpsd0) = at.noise.scipy_psd(y0, f_sample=sample_rate, nr_segments=4)
(ff1, fpsd1) = at.noise.scipy_psd(y1, f_sample=sample_rate, nr_segments=4)
(ff2, fpsd2) = at.noise.scipy_psd(y2, f_sample=sample_rate, nr_segments=4)
(ff3, fpsd3) = at.noise.scipy_psd(y3, f_sample=sample_rate, nr_segments=4)
(ff4, fpsd4) = at.noise.scipy_psd(y4, f_sample=sample_rate, nr_segments=4)
# compute frequency PSD prefactor h_a
a0 = x0.frequency_psd_from_qd(tau0)
a1 = x1.frequency_psd_from_qd(tau0)
a2 = x2.frequency_psd_from_qd(tau0)
a3 = x3.frequency_psd_from_qd(tau0)
a4 = x4.frequency_psd_from_qd(tau0)
# compute ADEV
(t0, d0, e, n) = at.oadev(x0.time_series, rate=sample_rate)
(t1, d1, e, n) = at.oadev(x1.time_series, rate=sample_rate)
(t2, d2, e, n) = at.oadev(x2.time_series, rate=sample_rate)
(t3, d3, e, n) = at.oadev(x3.time_series, rate=sample_rate)
(t4, d4, e, n) = at.oadev(x4.time_series, rate=sample_rate)
# compute MDEV
(mt0, md0, e, n) = at.mdev(x0.time_series, rate=sample_rate)
(mt1, md1, e, n) = at.mdev(x1.time_series, rate=sample_rate)
(mt2, md2, e, n) = at.mdev(x2.time_series, rate=sample_rate)
(mt3, md3, e, n) = at.mdev(x3.time_series, rate=sample_rate)
(mt4, md4, e, n) = at.mdev(x4.time_series, rate=sample_rate)
plt.figure()
# Phase PSD figure
plt.subplot(2, 2, 1)
plt.loglog(f0, [g0 * pow(xx, 0.0) for xx in f0],
'--',
label=r'$g_0f^0$',
color='black')
plt.loglog(f0, psd0, '.', color='black')
plt.loglog(f1[1:], [g1 * pow(xx, -1.0) for xx in f1[1:]],
'--',
label=r'$g_{-1}f^{-1}$',
color='red')
plt.loglog(f1, psd1, '.', color='red')
plt.loglog(f2[1:], [g2 * pow(xx, -2.0) for xx in f2[1:]],
'--',
label=r'$g_{-2}f^{-2}$',
color='green')
plt.loglog(f2, psd2, '.', color='green')
plt.loglog(f3[1:], [g3 * pow(xx, -3.0) for xx in f3[1:]],
'--',
label=r'$g_{-3}f^{-3}$',
color='pink')
plt.loglog(f3, psd3, '.', color='pink')
plt.loglog(f4[1:], [g4 * pow(xx, -4.0) for xx in f4[1:]],
'--',
label=r'$g_{-4}f^{-4}$',
color='blue')
plt.loglog(f4, psd4, '.', color='blue')
plt.grid()
plt.legend(framealpha=0.9)
plt.title(r'Phase Power Spectral Density')
plt.xlabel(r'Frequency (Hz)')
plt.ylabel(r' $S_x(f)$ $(s^2/Hz)$')
# frequency PSD figure
plt.subplot(2, 2, 2)
plt.loglog(ff0[1:], [a0 * pow(xx, 2) for xx in ff0[1:]],
'--',
label=r'$h_{2}f^{2}$',
color='black')
plt.loglog(ff0, fpsd0, '.', color='black')
plt.loglog(ff1[1:], [a1 * pow(xx, 1) for xx in ff1[1:]],
'--',
label=r'$h_{1}f^{1}$',
color='red')
plt.loglog(ff1, fpsd1, '.', color='red')
plt.loglog(ff2[1:], [a2 * pow(xx, 0) for xx in ff2[1:]],
'--',
label=r'$h_{0}f^{0}$',
color='green')
plt.loglog(ff2, fpsd2, '.', color='green')
plt.loglog(ff3[1:], [a3 * pow(xx, -1) for xx in ff3[1:]],
'--',
label=r'$h_{-1}f^{-1}$',
color='pink')
plt.loglog(ff3, fpsd3, '.', color='pink')
plt.loglog(ff4[1:], [a4 * pow(xx, -2) for xx in ff4[1:]],
'--',
label=r'$h_{-2}f^{-2}$',
color='blue')
plt.loglog(ff4, fpsd4, '.', color='blue')
plt.grid()
plt.legend(framealpha=0.9)
plt.title(r'Frequency Power Spectral Density')
plt.xlabel(r'Frequency (Hz)')
plt.ylabel(r' $S_y(f)$ $(1/Hz)$')
# ADEV figure
plt.subplot(2, 2, 3)
plt.loglog(t0, [x0.adev_from_qd(tau0, xx) / xx for xx in t0],
'--',
label=r'$\propto\sqrt{h_{2}}\tau^{-1}$',
color='black')
plt.loglog(t0, d0, 'o', color='black')
plt.loglog(t1, [x1.adev_from_qd(tau0, xx) / xx for xx in t1],
'--',
label=r'$\propto\sqrt{h_{1}}\tau^{-1}$',
color='red')
plt.loglog(t1, d1, 'o', color='red')
plt.loglog(t2, [x2.adev_from_qd(tau0, xx) / math.sqrt(xx) for xx in t2],
'--',
label=r'$\propto\sqrt{h_{0}}\tau^{-1/2}$',
color='green')
plt.loglog(t2, d2, 'o', color='green')
plt.loglog(t3, [x3.adev_from_qd(tau0, xx) * 1 for xx in t3],
'--',
label=r'$\propto\sqrt{h_{-1}}\tau^0$',
color='pink')
plt.loglog(t3, d3, 'o', color='pink')
plt.loglog(t4, [x4.adev_from_qd(tau0, xx) * math.sqrt(xx) for xx in t4],
'--',
label=r'$\propto\sqrt{h_{-2}}\tau^{+1/2}$',
color='blue')
plt.loglog(t4, d4, 'o', color='blue')
plt.legend(framealpha=0.9, loc='lower left')
plt.grid()
plt.title(r'Allan Deviation')
plt.xlabel(r'$\tau$ (s)')
plt.ylabel(r'ADEV')
# MDEV
plt.subplot(2, 2, 4)
plt.loglog(t0,
[x0.mdev_from_qd(tau0, xx) / pow(xx, 3.0 / 2.0) for xx in t0],
'--',
label=r'$\propto\sqrt{h_{2}}\tau^{-3/2}$',
color='black')
plt.loglog(mt0, md0, 'o', color='black')
plt.loglog(t1, [x1.mdev_from_qd(tau0, xx) / xx for xx in t1],
'--',
label=r'$\propto\sqrt{h_{1}}\tau^{-1}$',
color='red')
plt.loglog(mt1, md1, 'o', color='red')
plt.loglog(t2, [x2.mdev_from_qd(tau0, xx) / math.sqrt(xx) for xx in t2],
'--',
label=r'$\propto\sqrt{h_{0}}\tau^{-1/2}$',
color='green')
plt.loglog(mt2, md2, 'o', color='green')
plt.loglog(t3, [x3.mdev_from_qd(tau0, xx)**1 for xx in t3],
'--',
label=r'$\propto\sqrt{h_{-1}}\tau^0$',
color='pink')
plt.loglog(mt3, md3, 'o', color='pink')
plt.loglog(t4, [x4.mdev_from_qd(tau0, xx) * math.sqrt(xx) for xx in t4],
'--',
label=r'$\propto\sqrt{h_{-2}}\tau^{+1/2}$',
color='blue')
plt.loglog(mt4, md4, 'o', color='blue')
plt.legend(framealpha=0.9, loc='lower left')
plt.grid()
plt.title(r'Modified Allan Deviation')
plt.xlabel(r'$\tau$ (s)')
plt.ylabel(r'MDEV')
plt.show()