Time-domain phase fitting works almost
Except that the initial guess seems to massively impact the fitted phase. If the initial_phase is submitted, it seems to fit quite fine
This commit is contained in:
parent
3e8f3f713b
commit
bca152c9cd
|
|
@ -9,20 +9,22 @@ Then fit in t-domain to resolve \\varphi_0
|
|||
"""
|
||||
|
||||
import matplotlib.pyplot as plt
|
||||
import matplotlib.gridspec as gridspec
|
||||
import numpy as np
|
||||
if not True:
|
||||
import numpy.fft as ft
|
||||
else:
|
||||
import scipy.fftpack as ft
|
||||
import scipy.optimize as opt
|
||||
from scipy.signal import hilbert
|
||||
|
||||
|
||||
from mylib import *
|
||||
|
||||
rng = np.random.default_rng()
|
||||
|
||||
def guess_sine_parameters(samples, fft=None, fft_freqs=None, guess=[None,None,None,None]):
|
||||
"""Use crude methods to guess the parameters to a sine wave
|
||||
"""
|
||||
Use crude methods to guess the parameters to a sine wave
|
||||
from properties of both samples and their fourier transform.
|
||||
|
||||
Parameters:
|
||||
|
|
@ -31,13 +33,13 @@ def guess_sine_parameters(samples, fft=None, fft_freqs=None, guess=[None,None,No
|
|||
|
||||
guess - arraylike or float or None
|
||||
If float, this is interpreted as a frequency
|
||||
Order of parameters: [amplitude, frequency, phase, offset]
|
||||
Order of parameters: [amplitude, frequency, phase, baseline]
|
||||
If one parameter is None, it is filled with an approximate value if available.
|
||||
|
||||
Returns:
|
||||
-----------
|
||||
guess - arraylike
|
||||
An updated version of init_guess: [amplitude, frequency, phase, offset]
|
||||
An updated version of init_guess: [amplitude, frequency, phase, baseline]
|
||||
"""
|
||||
|
||||
if not hasattr(guess, '__len__'):
|
||||
|
|
@ -68,30 +70,20 @@ def guess_sine_parameters(samples, fft=None, fft_freqs=None, guess=[None,None,No
|
|||
continue
|
||||
|
||||
if i == 0: # amplitude
|
||||
guess[i] = np.std(samples) * (2 ** 1/2)
|
||||
if False:
|
||||
guess[i] = np.std(samples) * (2 ** 1/2)
|
||||
else:
|
||||
guess[i] = max(samples-np.mean(samples))
|
||||
elif i == 1: # frequency
|
||||
guess[i] = nearest_f
|
||||
elif i == 2: # phase
|
||||
guess[i] = nearest_phase
|
||||
elif i == 3: # offset samples
|
||||
elif i == 3: # baseline samples
|
||||
guess[i] = np.mean(samples)
|
||||
|
||||
return guess
|
||||
|
||||
def curvefit_sine(time, samples, init_guess, fitfunc=sine_fitfunc, bounds=(-np.inf, np.inf), **curve_kwargs):
|
||||
"""Fit a sine to samples with a supplied initial guess.
|
||||
|
||||
This function sets bounds for the phase.
|
||||
"""
|
||||
if bounds is None or bounds == (-np.inf, np.inf):
|
||||
high_bounds = np.array([np.inf, np.inf, +1*np.pi, np.inf])
|
||||
low_bounds = -1*high_bounds
|
||||
|
||||
bounds = (low_bounds, high_bounds)
|
||||
|
||||
return opt.curve_fit(fitfunc, time, samples, p0=init_guess, bounds=bounds, **curve_kwargs)
|
||||
|
||||
def fit_sine_to_samples(time, samples, samplerate=1, bandpass=None, guess=[None,None,None,None], fitfunc=sine_fitfunc, fft=None, freqs=None,**curve_kwargs):
|
||||
def fit_sine_to_samples(time, samples, samplerate=1, bandpass=None, guess=[None,None,None,None], fitfunc=sine_fitfunc, fft=None, freqs=None, bounds=None, restrained_fit=False, **curve_kwargs):
|
||||
if bandpass is not None or guess[1] is None or guess[2] is None:
|
||||
if fft is None:
|
||||
fft = ft.rfft(samples)
|
||||
|
|
@ -102,14 +94,64 @@ def fit_sine_to_samples(time, samples, samplerate=1, bandpass=None, guess=[None,
|
|||
fft[(freqs < bandpass[0]) | (freqs > bandpass[1])] = 0
|
||||
samples = ft.irfft(fft, samples.size)
|
||||
|
||||
old_guess = guess.copy()
|
||||
guess = guess_sine_parameters(samples, fft=fft, fft_freqs=freqs, guess=guess)
|
||||
|
||||
guess = np.array(guess)
|
||||
|
||||
if restrained_fit:
|
||||
# Restrained fit
|
||||
# only allow phase to be fitted
|
||||
# Take the amplitude from the hilbert envelope of the (bandpassed) samples
|
||||
|
||||
# References for lambda
|
||||
|
||||
frequency = guess[1]
|
||||
baseline = guess[3]
|
||||
envelope = np.abs(hilbert(samples))
|
||||
base_fitfunc = fitfunc
|
||||
|
||||
samples = samples/envelope
|
||||
|
||||
fitfunc = lambda t, amplitude, phase: base_fitfunc(t, amp=amplitude, phase=phase, freq=frequency, baseline=baseline)
|
||||
|
||||
old_guess = guess.copy()
|
||||
|
||||
guess = guess[[0,2]]
|
||||
|
||||
if bounds is None:
|
||||
sample_max = max(samples)
|
||||
|
||||
low_bounds = np.array([0.8,-np.pi])
|
||||
high_bounds = np.array([1.2, np.pi])
|
||||
else:
|
||||
low_bounds = bounds[0][[0,2]]
|
||||
high_bounds = bounds[1][[0,2]]
|
||||
|
||||
bounds = (low_bounds, high_bounds)
|
||||
|
||||
elif bounds is None :
|
||||
high_bounds = np.array([np.inf, np.inf, +1*np.pi, np.inf])
|
||||
low_bounds = -1*high_bounds
|
||||
|
||||
bounds = (low_bounds, high_bounds)
|
||||
|
||||
print(bounds, guess)
|
||||
|
||||
try:
|
||||
fit = curvefit_sine(time, samples, guess, fitfunc=fitfunc, **curve_kwargs)
|
||||
fit = opt.curve_fit(fitfunc, time, samples, p0=guess, bounds=bounds, **curve_kwargs)
|
||||
except RuntimeError:
|
||||
fit = None
|
||||
|
||||
if len(bounds[0]) == 1 or restrained_fit:
|
||||
# Restrained fitting was used
|
||||
# merge back into guess and fit
|
||||
|
||||
guess = old_guess
|
||||
fit = [
|
||||
np.array([fit[0][0], old_guess[1], fit[0][1], old_guess[3]]),
|
||||
fit[1]
|
||||
]
|
||||
|
||||
return fit, guess, (fft, freqs, samples)
|
||||
|
||||
def chi_sq(observed, expected):
|
||||
|
|
@ -125,7 +167,8 @@ def simulate_noisy_sine_fitting_SNR_and_residuals(
|
|||
N=1, snr_band=passband(), noise_band=passband(),
|
||||
t_length=1e-6, f_sample=250e6,
|
||||
noise_sigma=1, init_params=[1, 50e6, None, 0],
|
||||
show_original_signal_figure=True, show_bandpassed_signal_figure=True
|
||||
show_original_signal_figure=False, show_bandpassed_signal_figure=True,
|
||||
restrained_fit=True
|
||||
):
|
||||
residuals = np.empty( (int(N), len(init_params)) )
|
||||
real_snrs = np.empty( (int(N)) )
|
||||
|
|
@ -137,12 +180,13 @@ def simulate_noisy_sine_fitting_SNR_and_residuals(
|
|||
print("Iteration {} running".format(j))
|
||||
|
||||
# set random phase
|
||||
init_params[2] = 2*np.pi*rng.random()
|
||||
init_params[2] = phasemod(2*np.pi*rng.random())
|
||||
|
||||
samples = sine_fitfunc(time, *init_params)
|
||||
noise = None
|
||||
if noise_sigma: # noise
|
||||
noise = rng.normal(0,noise_sigma, size=(len(samples)))
|
||||
else:
|
||||
noise = np.zeros(len(samples))
|
||||
|
||||
real_snrs[j] = signal_to_noise(samples, noise, signal_band=snr_band, samplerate=f_sample, noise_band=noise_band)
|
||||
|
||||
|
|
@ -162,7 +206,13 @@ def simulate_noisy_sine_fitting_SNR_and_residuals(
|
|||
|
||||
axs1[1].legend()
|
||||
|
||||
fit, guess, (fft, freqs, bandpassed) = fit_sine_to_samples(time, samples+noise, f_sample, guess=[None,f_sine,None,None], bandpass=snr_band)
|
||||
if False:
|
||||
# use initial_params as guess
|
||||
guess = init_params
|
||||
else:
|
||||
guess = [None, f_sine, None, None]
|
||||
fit, guess, (fft, freqs, bandpassed) = fit_sine_to_samples(time, samples+noise, f_sample, guess=guess, bandpass=snr_band, restrained_fit=restrained_fit)
|
||||
|
||||
|
||||
if fit is None:
|
||||
residuals[j] = np.nan
|
||||
|
|
@ -170,27 +220,75 @@ def simulate_noisy_sine_fitting_SNR_and_residuals(
|
|||
|
||||
residuals[j] = normalise_sine_params(init_params - fit[0])
|
||||
|
||||
# figures
|
||||
if show_bandpassed_signal_figure and (j==0 or N == 1):
|
||||
fitted_sine = sine_fitfunc(time, *fit[0])
|
||||
analytic_signal = hilbert(bandpassed)
|
||||
envelope = np.abs(analytic_signal)
|
||||
instant_phase = np.angle(analytic_signal)
|
||||
|
||||
fig2, axs2 = plot_signal_and_spectrum(
|
||||
bandpassed, f_sample, "Bandpassed samples\nS/N:{:.2e}".format(real_snrs[j]),
|
||||
freq_unit='MHz', freq_scaler=freq_scaler
|
||||
)
|
||||
for ax in axs2[[1,2]]:
|
||||
ax.axvline(f_sine/freq_scaler, color='r', alpha=0.4) # f_beacon
|
||||
ax.axvspan(snr_band[0]/freq_scaler,snr_band[1]/freq_scaler, color='purple', alpha=0.3, label='signalband') # snr
|
||||
ax.axvspan(noise_band[0]/freq_scaler, noise_band[1]/freq_scaler, color='orange', alpha=0.3, label='noiseband') # noise_band
|
||||
fit_params = fit[0].tolist()
|
||||
fit_params[0] = envelope
|
||||
fitted_sine = sine_fitfunc(time, *fit_params)
|
||||
|
||||
l = axs2[0].plot(time, fitted_sine, label='fit')
|
||||
axs2[0].text(1, 1, '$\chi/d.o.f. = {:.2e}/{:.2e}$'.format(chi_sq(fitted_sine, samples), dof(samples,4)), transform=axs2[0].transAxes, ha='right', va='top')
|
||||
|
||||
# indicate initial phase
|
||||
axs2[2].axhline(init_params[2], color='r', alpha=0.4)
|
||||
axs2[2].axhline(init_params[2], color=l[0].get_color(), alpha=0.4)
|
||||
if False:
|
||||
fig4, axs4 = plt.subplots(2,1, sharex=True)
|
||||
fig4.suptitle("Bandpassed Hilbert")
|
||||
axs4[1].set_xlabel("Time")
|
||||
|
||||
axs2[0].legend(loc='upper left')
|
||||
axs2[1].legend()
|
||||
axs4[0].set_ylabel("Instant Phase")
|
||||
axs4[0].plot(time, instant_phase, marker='.')
|
||||
#axs4[0].axhline(init_params[2], color='r')
|
||||
|
||||
|
||||
axs4[1].set_ylabel("Instant Freq")
|
||||
axs4[1].plot(time[1:], np.diff(np.unwrap(instant_phase)) / (2*np.pi*f_sample), marker='.')
|
||||
#axs4[1].axhline(init_params[1], color='r')
|
||||
|
||||
|
||||
## Next figure
|
||||
if True:
|
||||
fig2, axs2 = plot_signal_and_spectrum(
|
||||
bandpassed, f_sample, "Bandpassed samples\nS/N:{:.2e}".format(real_snrs[j]),
|
||||
freq_unit='MHz', freq_scaler=freq_scaler,
|
||||
signal_kwargs=dict(alpha=0.8, time_unit='us')
|
||||
)
|
||||
for ax in axs2[[1,2]]:
|
||||
ax.axvline(f_sine/freq_scaler, color='r', alpha=0.4) # f_beacon
|
||||
ax.axvspan(snr_band[0]/freq_scaler,snr_band[1]/freq_scaler, color='purple', alpha=0.3, label='signalband') # snr
|
||||
ax.axvspan(noise_band[0]/freq_scaler, noise_band[1]/freq_scaler, color='orange', alpha=0.3, label='noiseband') # noise_band
|
||||
|
||||
l = axs2[0].plot(time, fitted_sine, label='fit', alpha=0.8)
|
||||
#axs2[0].text(1, 1, '$\chi/d.o.f. = {:.2e}/{:.2e}$'.format(chi_sq(fitted_sine, samples), dof(samples,4)), transform=axs2[0].transAxes, ha='right', va='top')
|
||||
|
||||
axs2[0].plot(time, envelope, label='envelope')
|
||||
|
||||
# indicate initial phase
|
||||
axs2[2].axhline(init_params[2], color='r', alpha=0.4)
|
||||
axs2[2].axhline(fit[0][2], color=l[0].get_color(), alpha=0.4)
|
||||
|
||||
axs2[0].legend(loc='upper left')
|
||||
axs2[1].legend()
|
||||
|
||||
|
||||
if True:
|
||||
fig5, axs5 = plt.subplots(2,1, sharex=True)
|
||||
fig5.suptitle("Bandpassed Samples vs Model")
|
||||
axs5[0].set_ylabel("Amplitude")
|
||||
axs5[0].plot(bandpassed, label='samples', alpha=0.8)
|
||||
axs5[0].plot(fitted_sine, label='fit', alpha=0.8)
|
||||
axs5[0].plot(envelope, label='envelope')
|
||||
|
||||
axs5[0].plot(samples, label='orig sine', alpha=0.8)
|
||||
|
||||
axs5[0].legend()
|
||||
|
||||
axs5[1].set_ylabel("Residuals")
|
||||
axs5[1].set_xlabel("Sample")
|
||||
axs5[1].plot(samples - fitted_sine, label="Sine - Model", alpha=0.8)
|
||||
axs5[1].plot(bandpassed - fitted_sine, label="Bandpassed - Model", alpha=0.8)
|
||||
|
||||
axs5[1].legend()
|
||||
|
||||
print("init:", init_params)
|
||||
print("fit :", fit[0])
|
||||
|
|
@ -203,32 +301,34 @@ if __name__ == "__main__":
|
|||
from argparse import ArgumentParser
|
||||
from myscriptlib import save_all_figs_to_path_or_show
|
||||
|
||||
rng = np.random.default_rng(1)
|
||||
|
||||
parser = ArgumentParser(description=__doc__)
|
||||
parser.add_argument("fname", metavar="path/to/figure[/]", nargs="?", help="Location for generated figure, will append __file__ if a directory. If not supplied, figure is shown.")
|
||||
parser.add_argument("-n", "--n-rand", dest='N', default=1, type=int, nargs='?', help='Number of random sines to fit')
|
||||
parser.add_argument('--seed', default=1, type=int, help='RNG seed')
|
||||
args = parser.parse_args()
|
||||
default_extensions = ['.pdf', '.png']
|
||||
|
||||
if args.fname == 'none':
|
||||
args.fname = None
|
||||
|
||||
rng = np.random.default_rng(args.seed)
|
||||
|
||||
report_N_nan = True
|
||||
restrained_fitting = True
|
||||
|
||||
f_sine = 53.123456 # MHz
|
||||
sine_amplitude = 0.2
|
||||
sine_offset = 0
|
||||
init_params = np.array([sine_amplitude, f_sine, None, sine_offset])
|
||||
sine_amplitude = 1
|
||||
sine_baseline = 0
|
||||
init_params = np.array([sine_amplitude, f_sine, None, sine_baseline])
|
||||
|
||||
N = int(args.N)
|
||||
f_sample = 250 # MHz
|
||||
t_length = 10 # us
|
||||
noise_sigma = 1
|
||||
noise_sigma = 0.01
|
||||
|
||||
f_delta = 1/t_length
|
||||
noise_band = (30,80) # MHz
|
||||
snr_band = (f_sine -2*f_delta, f_sine + 2*f_delta)
|
||||
snr_band = (f_sine -50*f_delta, f_sine + 50*f_delta)
|
||||
|
||||
time = sampled_time(f_sample, end=t_length)
|
||||
|
||||
|
|
@ -236,7 +336,7 @@ if __name__ == "__main__":
|
|||
|
||||
###### End of inputs
|
||||
|
||||
residuals, real_snrs, _ = simulate_noisy_sine_fitting_SNR_and_residuals(N=N, snr_band=snr_band, noise_band=noise_band, t_length=t_length, f_sample=f_sample, noise_sigma=noise_sigma, init_params=init_params)
|
||||
residuals, real_snrs, _ = simulate_noisy_sine_fitting_SNR_and_residuals(N=N, snr_band=snr_band, noise_band=noise_band, t_length=t_length, f_sample=f_sample, noise_sigma=noise_sigma, init_params=init_params, restrained_fit=restrained_fitting)
|
||||
|
||||
# Filter NaNs from fit attempts that failed
|
||||
nan_mask = ~np.isnan(residuals).any(axis=1)
|
||||
|
|
@ -248,26 +348,43 @@ if __name__ == "__main__":
|
|||
real_snrs = real_snrs [ nan_mask ]
|
||||
|
||||
## Plot Signal-to-Noise vs Residuals of the fit paramters
|
||||
fig, axs = plt.subplots(1,4, sharey=True)
|
||||
fig.suptitle("S/N vs Residuals, S/N Band ({:.2e},{:.2e})MHz".format(snr_band[0]/freq_scaler, snr_band[-1]/freq_scaler))
|
||||
fig, axs = plt.subplots(1,1 + 2*( not restrained_fitting), sharey=True)
|
||||
|
||||
if not hasattr(axs,'__len__'):
|
||||
axs = [axs]
|
||||
|
||||
fig.suptitle("S/N vs Residuals\nS/N Band ({:.2e},{:.2e})MHz \namp/sigma: {}".format(snr_band[0]/freq_scaler, snr_band[-1]/freq_scaler, sine_amplitude/ noise_sigma))
|
||||
axs[0].set_ylabel("S/N")
|
||||
j = 0 # plot counter
|
||||
for i in range(len(init_params)):
|
||||
if restrained_fitting and i in [0,1,3]:
|
||||
continue
|
||||
|
||||
unit_scaler = [1, 1][i==1]
|
||||
unit_string = ['', '[MHz]'][i==1]
|
||||
xlabel = ["Amplitude", "Frequency", "Phase", "Offset"][i]
|
||||
xlabel = ["Amplitude", "Frequency", "Phase", "Baseline"][i]
|
||||
|
||||
axs[i].set_xlabel(xlabel + unit_string)
|
||||
axs[i].plot(residuals[:,i]/unit_scaler, real_snrs, ls='none', marker='o')
|
||||
if i == 2:
|
||||
#axis_pi_ticker(axs[j].xaxis)
|
||||
axs[j].set_xlim(-np.pi, np.pi)
|
||||
|
||||
|
||||
real_snrs[np.isnan(real_snrs)] = 1 # Show nan values
|
||||
|
||||
axs[j].set_xlabel(xlabel + unit_string)
|
||||
axs[j].plot(residuals[:,i]/unit_scaler, real_snrs, ls='none', marker='o', alpha=max(0.3, 1/len(real_snrs)))
|
||||
|
||||
j += 1
|
||||
|
||||
## Plot Histograms of the Residuals
|
||||
if True and N > 1:
|
||||
for j in range(len(init_params)):
|
||||
if j == 0 or j == 3:
|
||||
if j == 3 or restrained_fitting and j == 1 or j == 0:
|
||||
continue
|
||||
|
||||
unit_scaler = [1, freq_scaler][j==1]
|
||||
unit_string = ['', '[MHz]'][j==1]
|
||||
xlabel = ["Amplitude", "Frequency", "Phase", "Offset"][j]
|
||||
xlabel = ["Amplitude", "Frequency", "Phase", "Baseline"][j]
|
||||
|
||||
title = xlabel + " residuals"
|
||||
title += "\n"
|
||||
|
|
@ -290,7 +407,7 @@ if __name__ == "__main__":
|
|||
maj_div = max(1, 2**np.ceil(np.log2(np.pi/(xmax-xmin)) + 1 ))
|
||||
min_div = maj_div*12
|
||||
|
||||
axis_pi_ticker(ax.xaxis, major_divider=maj_div, minor_divider=min_div)
|
||||
#axis_pi_ticker(ax.xaxis, major_divider=maj_div, minor_divider=min_div)
|
||||
|
||||
# Plot histogram between phase and frequency
|
||||
if True and N > 10:
|
||||
|
|
|
|||
|
|
@ -16,12 +16,12 @@ def phasemod(phase, low=np.pi):
|
|||
# Alias phase_mod to phasemod
|
||||
phase_mod = phasemod
|
||||
|
||||
def sine_fitfunc(t, amp=1, freq=1, phase=0, off=0, t_delay=0):
|
||||
def sine_fitfunc(t, amp=1, freq=1, phase=0, baseline=0, t_delay=0):
|
||||
"""Simple sine wave for fitting purposes"""
|
||||
return amp*np.cos( 2*np.pi*freq*(t-t_delay) + phase) + off
|
||||
return amp*np.cos( 2*np.pi*freq*(t-t_delay) + phase) + baseline
|
||||
|
||||
def sin_delay(f, t, phase=0):
|
||||
return sine_fitfunc(t, amp=1, freq=f, phase=phase, off=1, t_delay=0)
|
||||
return sine_fitfunc(t, amp=1, freq=f, phase=phase, baseline=1, t_delay=0)
|
||||
|
||||
def sampled_time(sample_rate=1, start=0, end=1, offset=0):
|
||||
return offset + np.arange(start, end, 1/sample_rate)
|
||||
|
|
|
|||
Loading…
Reference in New Issue