WIP on Pulse Detection
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lib/util.py
21
lib/util.py
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@ -3,7 +3,10 @@ Various useful utilities (duh)
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"""
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import numpy as np
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import scipy.fft as ft
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try:
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import scipy.fft as ft
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except ImportError:
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import numpy.fft as ft
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def sampled_time(sample_rate=1, start=0, end=1, offset=0):
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return offset + np.arange(start, end, 1/sample_rate)
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@ -82,7 +85,7 @@ def fft_bandpass(signal, band, samplerate):
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return ft.irfft(fft, signal.size), (fft, freqs)
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def deltapeak(timelength=1e3, samplerate=1, offset=None, peaklength=1):
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def deltapeak(timelength=1e3, samplerate=1, offset=None, peaklength=1, rng=None):
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"""
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Generate a series of zeroes with a deltapeak.
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@ -108,7 +111,19 @@ def deltapeak(timelength=1e3, samplerate=1, offset=None, peaklength=1):
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offset_min = 0 if offset[0] is None else offset[0]
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offset_max = N_samples if offset[-1] is None else offset[-1]
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offset = (np.random.random(1)*(offset_max - offset_min)+offset_min).astype(int) % N_samples
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if 0 < offset_min < 1:
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offset_min *= N_samples
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if 0 < offset_max < 1:
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offset_max *= N_samples
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if rng is not None:
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rand = rng.random(1)
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else:
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rand = np.random.random(1)
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rand = np.asarray(rand)
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offset = (rand * (offset_max - offset_min)+offset_min).astype(int) % N_samples
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position = (offset + np.arange(0, peaklength)).astype(int) % N_samples
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@ -0,0 +1,242 @@
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#!/usr/bin/env python3
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from lib import util
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from scipy import signal, interpolate
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import matplotlib.pyplot as plt
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import numpy as np
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rng = np.random.default_rng()
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class Waveform:
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name = None
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time = None
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signal = None
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def __init__(signal, time=None, name=None, dt=None):
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self.signal = signal
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self.time = time
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self.name = name
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if self.time is None and dt is not None:
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self.time = dt * len(signal)
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def white_noise_realisation(N_samples, noise_sigma=1, rng=rng):
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return rng.normal(0, noise_sigma or 0, size=N_samples)
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def antenna_bp(trace, low_bp, high_bp, dt, order=3):
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# order < 6 for stability
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fs = 1/dt
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nyq = 1* fs
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low_bp = low_bp / nyq
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high_bp = high_bp / nyq
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bp_filter = signal.butter(order, [low_bp, high_bp], 'band', fs=fs)
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bandpassed = signal.lfilter(*bp_filter, trace)
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return bandpassed
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def my_correlation(in1, template):
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#
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in1_long = np.zeros( (len(in1)+2*len(template)) )
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in1_long[len(template):-len(template)] = in1
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# fill the template with zeros and copy template
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template_long = np.zeros_like(in1_long)
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template_long[len(template):2*len(template)] = template
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lags = np.arange(-len(template), len(in1) ) - len(template)
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# do the correlation jig
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corrs = np.zeros_like(lags, dtype=float)
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for i, l in enumerate(lags):
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lagged_template = np.roll(template_long, l)
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corrs[i] = np.dot(lagged_template, in1_long)
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return corrs, (in1_long, template_long, lags)
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def trace_upsampler(template_signal, trace, template_t, trace_t):
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template_dt = template_t[1] - template_t[0]
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trace_dt = trace_t[1] - trace_t[0]
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upsample_factor = trace_dt/template_dt
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upsampled_trace_N = np.ceil(len(trace) * upsample_factor)
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upsample_factor = int(upsample_factor)
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upsampled_trace_N = int(upsampled_trace_N)
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# upsample trace
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upsampled_trace = np.zeros(upsampled_trace_N)
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upsampled_trace[::upsample_factor] = trace
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#upsampled_t = np.arange(trace_t[0], trace_t[-1], template_dt)
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upsampled_t = template_dt * np.arange(len(upsampled_trace)) + trace_t[0]
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return upsampled_trace, upsampled_t
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def template_downsampler(template_signal, trace, template_t, trace_t, offset):
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pass
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if __name__ == "__main__":
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import os
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import matplotlib
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if os.name == 'posix' and "DISPLAY" not in os.environ:
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matplotlib.use('Agg')
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template_dt = 5e-2 # ns
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bp_freq = (30e-3, 80e-3) # GHz
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template_length = 100 # ns
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noise_sigma_factor = 1e1 # keep between 10 and 0.1
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antenna_dt = 2 # ns
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antenna_timelength = 2048 # ns
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_deltapeak = util.deltapeak(timelength=template_length, samplerate=1/template_dt, offset=10/template_dt)
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template_t = util.sampled_time(1/template_dt, start=0, end=template_length)
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template_signal = antenna_bp(_deltapeak[0], *bp_freq, (np.sqrt(antenna_dt/template_dt))*template_dt) # TODO: fix sqrt constant
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template_peak_time = template_t[_deltapeak[1]]
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if False: # show template
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fig, ax = plt.subplots()
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ax.set_title("Deltapeak and Bandpassed Template")
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ax.set_xlabel("Time [ns]")
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ax.set_ylabel("Amplitude")
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ax.plot(template_t, max(template_signal)*_deltapeak[0])
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ax.plot(template_t, template_signal)
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fig.savefig('figures/11_template_deltapeak.pdf')
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# receive at antenna
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antenna_t = util.sampled_time(1/antenna_dt, start=0, end=antenna_timelength)
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antenna_samplelength = len(antenna_t)
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## place the deltapeak signal at a random location
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antenna_true_signal, antenna_peak_location = util.deltapeak(timelength=antenna_timelength, samplerate=1/antenna_dt, offset=[0.2, 0.8], rng=rng)
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antenna_peak_time = antenna_t[antenna_peak_location]
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if not True: # flip polarisation
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antenna_true_signal *= -1
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## Add noise
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noise_amplitude = max(template_signal) * noise_sigma_factor
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noise_realisation = noise_amplitude * white_noise_realisation(len(antenna_true_signal))
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antenna_unfiltered_signal = antenna_true_signal + noise_realisation
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antenna_signal = antenna_bp(antenna_unfiltered_signal, *bp_freq, antenna_dt)
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true_time_offset = antenna_peak_time - template_peak_time
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if True: # show signals
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fig, axs = plt.subplots(2, sharex=True)
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axs[0].set_title("Antenna Waveform")
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axs[-1].set_xlabel("Time [ns]")
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axs[0].set_ylabel("Amplitude")
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axs[0].plot(antenna_t, antenna_signal, label='bandpassed w/ noise')
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axs[0].plot(antenna_t, antenna_unfiltered_signal, label='true signal w/ noise')
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axs[0].plot(antenna_t, antenna_true_signal, label='true signal w/o noise')
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axs[0].legend()
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axs[1].set_title("Template")
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axs[1].set_ylabel("Amplitude")
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axs[1].plot(template_t, template_signal, label='orig')
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axs[1].plot(template_t + true_time_offset, template_signal, label='moved orig')
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axs[1].legend()
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fig.savefig('figures/11_antenna_signals.pdf')
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if True: # zoom
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wx = 100
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x0 = true_time_offset
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old_xlims = axs[0].get_xlim()
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axs[0].set_xlim( x0-wx, x0+wx)
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fig.savefig('figures/11_antenna_signals_zoom.pdf')
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# restore
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axs[0].set_xlim(*old_xlims)
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if True: # upsampled trace
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upsampled_trace, upsampled_t = trace_upsampler(template_signal, antenna_signal, template_t, antenna_t)
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if True: # Show upsampled traces
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fig2, axs2 = plt.subplots(1, sharex=True)
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if not hasattr(axs2, '__len__'):
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axs2 = [axs2]
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axs2[-1].set_xlabel("Time [ns]")
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axs2[0].set_ylabel("Amplitude")
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axs2[0].plot(antenna_t, antenna_signal, marker='o', label='orig')
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axs2[0].plot(upsampled_t, upsampled_trace, label='upsampled')
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axs2[0].legend(loc='upper right')
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fig2.savefig('figures/11_upsampled.pdf')
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wx = 1e2
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x0 = upsampled_t[0] + wx - 5
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axs2[0].set_xlim(x0-wx, x0+wx)
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fig2.savefig('figures/11_upsampled_zoom.pdf')
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# determine correlations with arguments
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lag_dt = upsampled_t[1] - upsampled_t[0]
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corrs, (out1_signal, out2_template, lags) = my_correlation(upsampled_trace, template_signal)
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else: # downsampled template
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raise NotImplementedError
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corrs, (out1_signal, out2_signal, lags) = my_downsampling_correlation(template_signal, antenna_signal, template_t, antenna_t)
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lag_dt = upsampled_t[1] - upsampled_t[0]
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# Determine best correlation time
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idx = np.argmax(abs(corrs))
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best_sample_lag = lags[idx]
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best_time_lag = best_sample_lag * lag_dt
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if axs2:
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axs2[-1].axvline(best_time_lag, color='r', alpha=0.5, linewidth=2)
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# Show the final signals correlated
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if True:
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fig, axs = plt.subplots(3, sharex=True)
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ylabel_kwargs = dict(
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rotation=0,
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ha='right',
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va='center'
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)
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axs[-1].set_xlabel("Time [ns]")
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# Signal
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i=0
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axs[i].set_ylabel("Signal\nAmplitude", **ylabel_kwargs)
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axs[i].plot(antenna_t, antenna_signal)
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# Template
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i=1
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axs[i].set_ylabel("Template\nAmplitude", **ylabel_kwargs)
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for offset in [0, best_time_lag]:
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axs[i].axvline(offset + len(template_signal) * (template_t[1] - template_t[0]), color='g')
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axs[i].axvline(offset, color='g')
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axs[i].plot(offset + template_t, template_signal)
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# Correlation
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i=2
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axs[i].set_ylabel("Correlation", **ylabel_kwargs)
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axs[i].plot(lags * lag_dt, corrs)
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axs[i].axvline(best_time_lag, color='r', ls='--')
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if True: # zoom
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wx = len(template_signal) * (template_t[1] - template_t[0])/2
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t0 = best_time_lag
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for t in [t0-wx, t0+wx]:
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axs[2].axvline(t, color='g')
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fig.tight_layout()
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fig.legend()
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fig.savefig('figures/11_corrs.pdf')
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#
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time_residual = best_time_lag - true_time_offset
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print(time_residual, template_dt, antenna_dt)
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plt.show()
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@ -0,0 +1 @@
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../lib/
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