def test_noise():
N = 500
rate = 1.0
w = noise.white(N)
b = noise.brown(N)
v = noise.violet(N)
p = noise.pink(N)
assert len(w) == N
assert len(b) == N
assert len(v) == N - 1 # why?
assert len(p) == N
def test_noise():
N = 500
rate = 1.0
w = noise.white(N)
b = noise.brown(N)
v = noise.violet(N)
p = noise.pink(N)
assert len(w) == N
assert len(b) == N
assert len(v) == N-1 # why?
assert len(p) == N
def test_noise():
N = 500
#rate = 1.0
w = noise.white(N)
b = noise.brown(N)
v = noise.violet(N)
p = noise.pink(N)
# check output length
assert len(w) == N
assert len(b) == N
assert len(v) == N
assert len(p) == N
# check output type
for x in [w, b, v, p]:
assert type(x) == numpy.ndarray, "%s is not numpy.ndarray" % (type(x))
# white frequency modulation => 1/sqrt(tau) ADEV
print("White frequency noise - should have 1/sqrt(tau) ADEV")
freq_white = noise.white(N)
phase_rw = noise.brown(N) # integrate to get Brownian, or random walk phase
plotallan(plt, freq_white, 1, t, 'b.')
plotallan_phase(plt, phase_rw, 1, t, 'bo',label='random walk phase a.k.a. white frequency noise')
plotline(plt, -0.5, t, 'b',label="f^(-1/2)")
# pink phase noise => 1/tau ADEV and MDEV
print("Pink phase noise - should tau^(-3/2) MDEV")
phase_pink = noise.pink(N)
plotallan_phase(plt, phase_pink, 1, t, 'ko',label="pink/flicker phase noise")
plotline(plt, -1, t, 'k',label="f^(-1)")
# white phase noise => 1/tau ADEV and tau^(-3/2) MDEV
print("White phase noise - should have 1/tau ADEV")
phase_white = noise.white(N)
plotallan_phase(plt, phase_white, 1, t, 'ro',label="white phase noise")
freq_w = noise.violet(N) # diff to get frequency, "Violet noise"
plotallan(plt, freq_w, 1, t, 'r.')
plotline(plt, -1.5, t, 'r',label="f^(-3/2)")
plt.title('allantools noise type demo')
plt.xlabel('Tau')
plt.ylabel('Modified Allan deviation')
print("Done.")
plt.legend(loc="lower left", framealpha=0.7)
plt.grid()
plt.show()
t,
'bo',
label='random walk phase a.k.a. white frequency noise')
plotline(plt, -0.5, t, 'b', label="f^(-1/2)")
# pink phase noise => 1/tau ADEV and MDEV
print("Pink phase noise - should tau^(-3/2) MDEV")
phase_pink = noise.pink(N)
plotallan_phase(plt,
phase_pink,
1,
t,
'ko',
label="pink/flicker phase noise")
plotline(plt, -1, t, 'k', label="f^(-1)")
# white phase noise => 1/tau ADEV and tau^(-3/2) MDEV
print("White phase noise - should have 1/tau ADEV")
phase_white = noise.white(N)
plotallan_phase(plt, phase_white, 1, t, 'ro', label="white phase noise")
freq_w = noise.violet(N) # diff to get frequency, "Violet noise"
plotallan(plt, freq_w, 1, t, 'r.')
plotline(plt, -1.5, t, 'r', label="f^(-3/2)")
plt.title('allantools noise type demo')
plt.xlabel('Tau')
plt.ylabel('Modified Allan deviation')
print("Done.")
plt.legend(loc="lower left", framealpha=0.7)
plt.grid()
plt.show()
def test_psd2allan_figure():
f = np.arange(
1e4 + 1
) # generate f-vector 0...10^4 Hz in 1 Hz steps -> Nyquist freq is 5 kHz
S_y0 = 1e-24 # some arbitrarily chosen noise level
S_y_WFM = S_y0 * np.ones(
np.size(f)) # generate white frequency noise S_y(f)
S_y_WPM = S_y_WFM * f**2 # white phase noise S_y(f)
plt.rc('text', usetex=True)
plt.close('all')
plt.figure(1)
plt.loglog(f[f > 0], S_y_WFM[f > 0])
plt.loglog(f[f > 0], S_y_WPM[f > 0])
y_WFM_ind = noise.white(num_points=int(2e4), b0=S_y0, fs=2e4)
y_WPM_ind = noise.violet(num_points=int(2e4), b2=S_y0, fs=2e4)
f, S_y_WFM_ind = welch(y_WFM_ind,
fs=2e4,
nperseg=y_WFM_ind.size,
window='hanning')
f, S_y_WPM_ind = welch(y_WPM_ind,
fs=2e4,
nperseg=y_WPM_ind.size,
window='hanning')
plt.loglog(f, S_y_WFM_ind)
plt.loglog(f, S_y_WPM_ind)
plt.xlabel('$f$ [Hz]')
plt.ylabel('$S_y$')
plt.legend(('WFM direct', 'WPM direct', 'WFM indirect', 'WPM indirect'))
#(tau, sigma_WFM)= at.psd2allan(S_y_WFM, f, kind= 'a')
#(tau, sigma_WPM)= at.psd2allan(S_y_WPM, f, kind= 'a')
#(tau, modsigma_WFM)= at.psd2allan(S_y_WFM, f, kind= 'm')
#(tau, modsigma_WPM)= at.psd2allan(S_y_WPM, f, kind= 'm')
(tau, sigma_WFM) = at.psd2allan(S_y_WFM, kind='a')
(tau, sigma_WPM) = at.psd2allan(S_y_WPM, kind='a')
(tau, modsigma_WFM) = at.psd2allan(S_y_WFM, kind='m')
(tau, modsigma_WPM) = at.psd2allan(S_y_WPM, kind='m')
plt.figure(2)
plt.loglog(tau, sigma_WFM)
plt.loglog(tau, sigma_WPM)
plt.loglog(tau, modsigma_WFM)
plt.loglog(tau, modsigma_WPM)
(tau, sigma_WFM_ind) = at.psd2allan(S_y_WFM_ind, kind='a')
(tau, sigma_WPM_ind) = at.psd2allan(S_y_WPM_ind, kind='a')
(tau, modsigma_WFM_ind) = at.psd2allan(S_y_WFM_ind, kind='m')
(tau, modsigma_WPM_ind) = at.psd2allan(S_y_WPM_ind, kind='m')
plt.loglog(tau, sigma_WFM_ind, ':C0')
plt.loglog(tau, sigma_WPM_ind, ':C1')
plt.loglog(tau, modsigma_WFM_ind, ':C2')
plt.loglog(tau, modsigma_WPM_ind, ':C3')
f_h = 1e4
sigma_WFM_theo = np.sqrt(S_y0 / tau / 2.0)
sigma_WPM_theo = np.sqrt(3.0 * f_h * S_y0 / tau**2 / (2.0 * np.pi)**2)
modsigma_WFM_theo = np.sqrt(S_y0 / tau / 4.0)
modsigma_WPM_theo = np.sqrt(3.0 * S_y0 / tau**3 / (2.0 * np.pi)**2 / 2)
plt.loglog(tau, sigma_WFM_theo, '.C0')
plt.loglog(tau, sigma_WPM_theo, '.C1')
plt.loglog(tau, modsigma_WFM_theo, '.C2')
plt.loglog(tau, modsigma_WPM_theo, '.C3')
plt.xlabel(r'$\tau$ [s]')
plt.ylabel(r'$\sigma_y$')
plt.legend(
('psd2allan direct, ADEV, WFM', 'psd2allan direct, ADEV, WPM',
'psd2allan direct, modADEV, WFM', 'psd2allan direct, modADEV, WPM',
'psd2allan indirect, ADEV, WFM', 'psd2allan indirect, ADEV, WPM',
'psd2allan indirect, modADEV, WFM',
'psd2allan indirect, modADEV, WPM', 'theoretical, ADEV, WFM',
'theoretical, ADEV, WPM', 'theoretical, modADEV, WFM',
'theoretical, modADEV, WPM'))
