432 lines
15 KiB
Python
Executable File
432 lines
15 KiB
Python
Executable File
#!/usr/bin/env python3
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# vim: fdm=indent ts=4
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__doc__ = \
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"""
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Sample sine wave + noise
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Filter it
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Then fit in t-domain to resolve \\varphi_0
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"""
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import matplotlib.pyplot as plt
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import numpy as np
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if not True:
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import numpy.fft as ft
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else:
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import scipy.fftpack as ft
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import scipy.optimize as opt
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from scipy.signal import hilbert
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from mylib import *
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rng = np.random.default_rng()
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def guess_sine_parameters(samples, fft=None, fft_freqs=None, guess=[None,None,None,None]):
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"""
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Use crude methods to guess the parameters to a sine wave
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from properties of both samples and their fourier transform.
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Parameters:
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-----------
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samples - arraylike
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guess - arraylike or float or None
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If float, this is interpreted as a frequency
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Order of parameters: [amplitude, frequency, phase, baseline]
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If one parameter is None, it is filled with an approximate value if available.
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Returns:
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-----------
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guess - arraylike
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An updated version of init_guess: [amplitude, frequency, phase, baseline]
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"""
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if not hasattr(guess, '__len__'):
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# interpret as a frequency (might still be None)
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guess = [None, guess, None, None]
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assert len(guess) == 4, "Wrong length for initial guess (should be 4)"
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nearest_f, nearest_phase = None, None
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if fft is not None and (guess[1] is None or guess[2] is None):
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nearest_idx = None
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if guess[1] is not None:
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if fft_freqs is not None:
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nearest_idx = find_nearest(guess[1], fft_freqs)
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else:
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# We'll take the strongest peak by default
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if fft is not None:
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nearest_idx = np.argmax(fft*2)
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if nearest_idx is not None:
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if fft_freqs is not None:
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nearest_f = fft_freqs[nearest_idx]
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nearest_phase = np.angle(fft[nearest_idx])
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for i in range(4):
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if guess[i] is not None:
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continue
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if i == 0: # amplitude
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if False:
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guess[i] = np.std(samples) * (2 ** 1/2)
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else:
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guess[i] = max(samples-np.mean(samples))
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elif i == 1: # frequency
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guess[i] = nearest_f
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elif i == 2: # phase
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guess[i] = nearest_phase
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elif i == 3: # baseline samples
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guess[i] = np.mean(samples)
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return guess
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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):
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if bandpass is not None or guess[1] is None or guess[2] is None:
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if fft is None:
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fft = ft.rfft(samples)
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if freqs is None:
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freqs = ft.rfftfreq(samples.size, 1/samplerate)
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if bandpass:
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fft[(freqs < bandpass[0]) | (freqs > bandpass[1])] = 0
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samples = ft.irfft(fft, samples.size)
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guess = guess_sine_parameters(samples, fft=fft, fft_freqs=freqs, guess=guess)
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guess = np.array(guess)
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if restrained_fit:
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# Restrained fit
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# only allow phase to be fitted
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# Take the amplitude from the hilbert envelope of the (bandpassed) samples
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# References for lambda
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frequency = guess[1]
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baseline = guess[3]
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envelope = np.abs(hilbert(samples))
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base_fitfunc = fitfunc
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samples = samples/envelope
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fitfunc = lambda t, amplitude, phase: base_fitfunc(t, amp=amplitude, phase=phase, freq=frequency, baseline=baseline)
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old_guess = guess.copy()
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guess = guess[[0,2]]
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if bounds is None:
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sample_max = max(samples)
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low_bounds = np.array([0.8,-np.pi])
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high_bounds = np.array([1.2, np.pi])
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else:
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low_bounds = bounds[0][[0,2]]
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high_bounds = bounds[1][[0,2]]
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bounds = (low_bounds, high_bounds)
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elif bounds is None :
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high_bounds = np.array([np.inf, np.inf, +1*np.pi, np.inf])
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low_bounds = -1*high_bounds
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bounds = (low_bounds, high_bounds)
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print(bounds, guess)
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try:
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fit = opt.curve_fit(fitfunc, time, samples, p0=guess, bounds=bounds, **curve_kwargs)
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except RuntimeError:
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fit = None
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if len(bounds[0]) == 1 or restrained_fit:
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# Restrained fitting was used
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# merge back into guess and fit
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guess = old_guess
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fit = [
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np.array([fit[0][0], old_guess[1], fit[0][1], old_guess[3]]),
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fit[1]
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]
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return fit, guess, (fft, freqs, samples)
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def chi_sq(observed, expected):
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"""
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Simple \Chi^2 test
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"""
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return np.sum( (observed-expected)**2 / expected)
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def dof(observed, n_parameters=1):
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return len(observed) - n_parameters
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def simulate_noisy_sine_fitting_SNR_and_residuals(
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N=1, snr_band=passband(), noise_band=passband(),
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t_length=1e-6, f_sample=250e6,
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noise_sigma=1, init_params=[1, 50e6, None, 0],
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show_original_signal_figure=False, show_bandpassed_signal_figure=True,
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restrained_fit=True
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):
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residuals = np.empty( (int(N), len(init_params)) )
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real_snrs = np.empty( (int(N)) )
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axs1, axs2 = None, None
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for j, _ in enumerate(residuals):
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if j % 500 == 0:
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print("Iteration {} running".format(j))
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# set random phase
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init_params[2] = phasemod(2*np.pi*rng.random())
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samples = sine_fitfunc(time, *init_params)
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if noise_sigma: # noise
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noise = rng.normal(0,noise_sigma, size=(len(samples)))
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else:
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noise = np.zeros(len(samples))
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real_snrs[j] = signal_to_noise(samples, noise, signal_band=snr_band, samplerate=f_sample, noise_band=noise_band)
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# plot original
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if show_original_signal_figure and (j==0 or N == 1):
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fig, axs1 = plot_signal_and_spectrum(
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samples+noise, f_sample, "Original",
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freq_unit='MHz', freq_scaler=freq_scaler
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)
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for ax in axs1[[1,2]]:
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ax.axvline(f_sine/freq_scaler, color='r', alpha=0.4) # f_beacon
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ax.axvspan(snr_band[0]/freq_scaler,snr_band[1]/freq_scaler, color='purple', alpha=0.3, label='signalband') # snr
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ax.axvspan(noise_band[0]/freq_scaler, noise_band[1]/freq_scaler, color='orange', alpha=0.3, label='noiseband') # noise_band
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# indicate initial phase
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axs1[2].axhline(init_params[2], color='r', alpha=0.4)
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axs1[1].legend()
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if False:
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# use initial_params as guess
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guess = init_params
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else:
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guess = [None, f_sine, None, None]
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fit, guess, (fft, freqs, bandpassed) = fit_sine_to_samples(time, samples+noise, f_sample, guess=guess, bandpass=snr_band, restrained_fit=restrained_fit)
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if fit is None:
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residuals[j] = np.nan
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continue
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residuals[j] = normalise_sine_params(init_params - fit[0])
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# figures
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if show_bandpassed_signal_figure and (j==0 or N == 1):
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analytic_signal = hilbert(bandpassed)
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envelope = np.abs(analytic_signal)
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instant_phase = np.angle(analytic_signal)
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fit_params = fit[0].tolist()
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fit_params[0] = envelope
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fitted_sine = sine_fitfunc(time, *fit_params)
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if False:
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fig4, axs4 = plt.subplots(2,1, sharex=True)
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fig4.suptitle("Bandpassed Hilbert")
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axs4[1].set_xlabel("Time")
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axs4[0].set_ylabel("Instant Phase")
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axs4[0].plot(time, instant_phase, marker='.')
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#axs4[0].axhline(init_params[2], color='r')
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axs4[1].set_ylabel("Instant Freq")
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axs4[1].plot(time[1:], np.diff(np.unwrap(instant_phase)) / (2*np.pi*f_sample), marker='.')
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#axs4[1].axhline(init_params[1], color='r')
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## Next figure
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if True:
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fig2, axs2 = plot_signal_and_spectrum(
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bandpassed, f_sample, "Bandpassed samples\nS/N:{:.2e}".format(real_snrs[j]),
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freq_unit='MHz', freq_scaler=freq_scaler,
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signal_kwargs=dict(alpha=0.8, time_unit='us')
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)
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for ax in axs2[[1,2]]:
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ax.axvline(f_sine/freq_scaler, color='r', alpha=0.4) # f_beacon
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ax.axvspan(snr_band[0]/freq_scaler,snr_band[1]/freq_scaler, color='purple', alpha=0.3, label='signalband') # snr
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ax.axvspan(noise_band[0]/freq_scaler, noise_band[1]/freq_scaler, color='orange', alpha=0.3, label='noiseband') # noise_band
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l = axs2[0].plot(time, fitted_sine, label='fit', alpha=0.8)
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#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')
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axs2[0].plot(time, envelope, label='envelope')
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# indicate initial phase
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axs2[2].axhline(init_params[2], color='r', alpha=0.4)
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axs2[2].axhline(fit[0][2], color=l[0].get_color(), alpha=0.4)
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axs2[0].legend(loc='upper left')
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axs2[1].legend()
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if True:
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fig5, axs5 = plt.subplots(2,1, sharex=True)
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fig5.suptitle("Bandpassed Samples vs Model")
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axs5[0].set_ylabel("Amplitude")
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axs5[0].plot(bandpassed, label='samples', alpha=0.8)
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axs5[0].plot(fitted_sine, label='fit', alpha=0.8)
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axs5[0].plot(envelope, label='envelope')
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axs5[0].plot(samples, label='orig sine', alpha=0.8)
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axs5[0].legend()
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axs5[1].set_ylabel("Residuals")
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axs5[1].set_xlabel("Sample")
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axs5[1].plot(samples - fitted_sine, label="Sine - Model", alpha=0.8)
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axs5[1].plot(bandpassed - fitted_sine, label="Bandpassed - Model", alpha=0.8)
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axs5[1].legend()
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print("init:", init_params)
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print("fit :", fit[0])
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print("res :", residuals[j])
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return residuals, real_snrs, (axs1, axs2)
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if __name__ == "__main__":
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from argparse import ArgumentParser
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from myscriptlib import save_all_figs_to_path_or_show
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parser = ArgumentParser(description=__doc__)
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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.")
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parser.add_argument("-n", "--n-rand", dest='N', default=1, type=int, nargs='?', help='Number of random sines to fit')
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parser.add_argument('--seed', default=1, type=int, help='RNG seed')
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args = parser.parse_args()
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default_extensions = ['.pdf', '.png']
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if args.fname == 'none':
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args.fname = None
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rng = np.random.default_rng(args.seed)
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report_N_nan = True
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restrained_fitting = True
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f_sine = 53.123456 # MHz
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sine_amplitude = 1
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sine_baseline = 0
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init_params = np.array([sine_amplitude, f_sine, None, sine_baseline])
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N = int(args.N)
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f_sample = 250 # MHz
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t_length = 10 # us
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noise_sigma = 0.01
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f_delta = 1/t_length
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noise_band = (30,80) # MHz
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snr_band = (f_sine -50*f_delta, f_sine + 50*f_delta)
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time = sampled_time(f_sample, end=t_length)
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freq_scaler = 1
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###### End of inputs
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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)
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# Filter NaNs from fit attempts that failed
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nan_mask = ~np.isnan(residuals).any(axis=1)
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if report_N_nan:
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## report how many NaNs were found
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print("NaNs: {}/{}".format(np.count_nonzero(~nan_mask), len(real_snrs)))
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residuals = residuals[ nan_mask ]
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real_snrs = real_snrs [ nan_mask ]
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## Plot Signal-to-Noise vs Residuals of the fit paramters
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fig, axs = plt.subplots(1,1 + 2*( not restrained_fitting), sharey=True)
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if not hasattr(axs,'__len__'):
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axs = [axs]
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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))
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axs[0].set_ylabel("S/N")
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j = 0 # plot counter
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for i in range(len(init_params)):
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if restrained_fitting and i in [0,1,3]:
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continue
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unit_scaler = [1, 1][i==1]
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unit_string = ['', '[MHz]'][i==1]
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xlabel = ["Amplitude", "Frequency", "Phase", "Baseline"][i]
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if i == 2:
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#axis_pi_ticker(axs[j].xaxis)
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axs[j].set_xlim(-np.pi, np.pi)
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real_snrs[np.isnan(real_snrs)] = 1 # Show nan values
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axs[j].set_xlabel(xlabel + unit_string)
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axs[j].plot(residuals[:,i]/unit_scaler, real_snrs, ls='none', marker='o', alpha=max(0.3, 1/len(real_snrs)))
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j += 1
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## Plot Histograms of the Residuals
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if True and N > 1:
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for j in range(len(init_params)):
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if j == 3 or restrained_fitting and j == 1 or j == 0:
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continue
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unit_scaler = [1, freq_scaler][j==1]
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unit_string = ['', '[MHz]'][j==1]
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xlabel = ["Amplitude", "Frequency", "Phase", "Baseline"][j]
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title = xlabel + " residuals"
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title += "\n"
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title += "f: {:.2e}MHz, amp/sigma: {:.2e}".format(f_sine/freq_scaler, sine_amplitude/noise_sigma)
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if noise_band:
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title += " Band ({:.2e},{:.2e})MHz".format(noise_band[0]/freq_scaler, noise_band[1]/freq_scaler)
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fig, ax = plt.subplots()
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ax.set_title(title)
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ax.hist(residuals[:,j]/unit_scaler, density=False, histtype='step', bins='sqrt')
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ax.set_xlabel(xlabel + unit_string)
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ax.set_ylabel("Counts")
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# make it symmetric around 0
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xmax = max(*ax.get_xlim())
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ax.set_xlim(-xmax, xmax)
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if j == 2: # Phase
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xmin, xmax = ax.get_xlim()
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maj_div = max(1, 2**np.ceil(np.log2(np.pi/(xmax-xmin)) + 1 ))
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min_div = maj_div*12
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#axis_pi_ticker(ax.xaxis, major_divider=maj_div, minor_divider=min_div)
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# Plot histogram between phase and frequency
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if True and N > 10:
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fig, ax = plt.subplots()
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title = "Residuals\n"
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title += "f: {:.2e}MHz, amp/sigma: {:.2e}".format(f_sine/freq_scaler, sine_amplitude/noise_sigma)
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if noise_band:
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title += "\n Band ({},{})MHz".format(noise_band[0]/freq_scaler, noise_band[1]/freq_scaler)
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title += ", N={:.1e}".format(N)
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ax.set_title(title)
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ax.set_xlabel('Frequency [MHz]')
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ax.set_ylabel('Phase')
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_, _, _, sc = ax.hist2d(residuals[:,1]/freq_scaler, residuals[:,2], bins=np.sqrt(len(residuals)))
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fig.colorbar(sc, ax=ax, label='Counts')
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#ax.set_xlim(-np.pi, np.pi)
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axis_pi_ticker(ax.yaxis)
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ax.set_ylim(-np.pi, np.pi)
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## Save or show figures
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save_all_figs_to_path_or_show(args.fname, default_basename=__file__, default_extensions=default_extensions)
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