from pyboat import WAnalyzer, ssg
from pyboat import plotting as pl
# set up analyzing instance
periods = np.linspace(5, 60, 100)
dt = 1
wAn = WAnalyzer(periods, dt)
# create a bunch of chirp signals
# with diverging period over time
Nsignals = 50 # times 2
Tstart = 30 # initial period
Tmax = 50 # slowest signal
Nt = 500 # number of samples per signal
signals = [
ssg.create_noisy_chirp(T1=Tstart, T2=Tend, Nt=Nt, eps=1)
for Tend in np.linspace(Tstart, Tmax, Nsignals)
]
# add the same number of pure noise signals
noisy_ones = [ssg.ar1_sim(alpha=0.5, Nt=Nt) for i in range(Nsignals)]
# signals ids are just column numbers here
signals = pd.DataFrame(signals + noisy_ones).T
# get the the individual ridge readouts
ridge_results = {}
# store the individual time averaged Wavelet spectra
df_fouriers = pd.DataFrame(index=wAn.periods)
'''
from pyboat import WAnalyzer, ssg
from pyboat.plotting import plot_ensemble_dynamics, plot_power_distribution
# set up analyzing instance
periods = np.linspace(5, 60, 100)
dt = 1
wAn = WAnalyzer(periods, dt, T_cut_off=None)
# create a bunch of chirp signals
Nsignals = 50 # times 2
T1 = 30 # initial period
Nt = 500 # number of samples per signal
signals = [
ssg.create_noisy_chirp(T1=T1, T2=T, Nt=Nt, eps=1)
for T in np.linspace(T1, 50, Nsignals)
]
# add the same amount of pure noise
noisy_ones = [ssg.ar1_sim(alpha=0.5, N=Nt) for i in range(Nsignals)]
signals = signals + noisy_ones
# get the the individual ridge readouts
ridge_results = []
for signal in signals:
wAn.compute_spectrum(signal, sinc_detrend=False, do_plot=False)
rd = wAn.get_maxRidge(smoothing_wsize=11)
ridge_results.append(rd)
ppl.ion()
periods = np.linspace(4, 90, 150)
dt = 2
T_cut_off = 65 # cut off period
time_unit = 's'
# --- create a synthetic signal ---
eps = 0.5 # noise intensity
alpha = 0.4 # AR1 parameter
Nt = 500 # number of samples
signal1 = ssg.create_noisy_chirp(T1=30 / dt,
T2=50 / dt,
Nt=Nt,
eps=eps,
alpha=alpha)
# add slower oscillatory trend
signal2 = ssg.create_chirp(T1=70 / dt, T2=70 / dt, Nt=Nt)
# linear superposition
signal = signal1 + 1.5 * signal2
# --- calculate trend ---
trend = pyboat.sinc_smooth(signal, T_cut_off, dt)
detr_signal = signal - trend
# plot the signal/trend
# compare to the theoretical spectrum,
# note the finite size effects suppressing the power for higher periods!
theo_bg = ar1_powerspec(alpha, wAn.periods, wAn.dt)
ppl.plot(wAn.periods, theo_bg, 'k--', label='theoretical')
ppl.legend()
# now we take the median of the Fourier power
# distribution as expected empirical background
emp_bg = df_fouriers.median(axis=1)
# note that we have have persistent and consistent periods
print(len(emp_bg.index) == len(wAn.periods))
# let's create a very noisy signal with the same
# background process as noise mixed in
test_signal = ssg.create_noisy_chirp(T1=70, T2=40, Nt=500, alpha=alpha,
eps=1.) # SNR is 1!
# plain wavelet analysis
wAn.compute_spectrum(test_signal)
# let's draw the confidence intervals from the theoretical spectrum
wAn.draw_confidence_from_bg(theo_bg, colors='black')
# now let's use the 'empirical' one, taking into
# account the finite size effect
wAn.draw_confidence_from_bg(emp_bg, colors='orange')
# finally let's get the ridge within the CI regions
# from the empirical background
ridge_data = wAn.get_sign_maxRidge(emp_bg)
wAn.draw_Ridge()