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Pulse finding for multiple SNR
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1 changed files with 241 additions and 211 deletions
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@ -136,9 +136,9 @@ if __name__ == "__main__":
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bp_freq = (30e-3, 80e-3) # GHz
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template_dt = 5e-2 # ns
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template_length = 500 # ns
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noise_sigma_factor = 1e-1 # amplitude factor
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N_residuals = 50*3 if len(sys.argv) < 2 else int(sys.argv[1])
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noise_factors = [1e-4, 3e-4, 1e-3, 3e-3, 1e-2, 3e-2, 1e-1, 3e-1, 5e-1, 7e-1] # amplitude factor
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antenna_dt = 2 # ns
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antenna_timelength = 2048 # ns
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@ -176,254 +176,284 @@ if __name__ == "__main__":
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if True:
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plt.close(fig)
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#
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# Find difference between true and templated times
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#
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time_residuals = np.zeros(N_residuals)
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for j in tqdm(range(N_residuals)):
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do_plots = j==0
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time_accuracies = np.zeros(len(noise_factors))
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for k, noise_sigma_factor in tqdm(enumerate(noise_factors)):
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print() #separating tqdm
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#
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# Find difference between true and templated times
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#
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time_residuals = np.zeros(N_residuals)
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for j in tqdm(range(N_residuals)):
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do_plots = j==0
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# receive at antenna
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## place the deltapeak signal at a random location
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antenna = Waveform(None, dt=antenna_dt, name='Signal')
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# receive at antenna
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## place the deltapeak signal at a random location
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antenna = Waveform(None, dt=antenna_dt, name='Signal')
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if not True: # Create antenna trace without template
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antenna_true_signal, antenna_peak_sample = util.deltapeak(timelength=antenna_timelength, samplerate=1/antenna.dt, offset=[0.2, 0.8], rng=rng)
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if not True: # Create antenna trace without template
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antenna_true_signal, antenna_peak_sample = util.deltapeak(timelength=antenna_timelength, samplerate=1/antenna.dt, offset=[0.2, 0.8], rng=rng)
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antenna.peak_sample = antenna_peak_sample
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antenna.peak_time = antenna.dt * antenna.peak_sample
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antenna.signal = antenna_bp(antenna.signal, *bp_freq, antenna.dt)
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antenna.peak_sample = antenna_peak_sample
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antenna.peak_time = antenna.dt * antenna.peak_sample
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antenna.signal = antenna_bp(antenna.signal, *bp_freq, antenna.dt)
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print(f"Antenna Peak Time: {antenna.peak_time}")
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print(f"Antenna Peak Sample: {antenna.peak_sample}")
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else: # Sample the template at some offset
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antenna.peak_time = antenna_timelength * ((0.8 - 0.2) *rng.random(1) + 0.2)
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sampling_offset = rng.random(1)*antenna.dt
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else: # Sample the template at some offset
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antenna.peak_time = antenna_timelength * ((0.8 - 0.2) *rng.random(1) + 0.2)
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sampling_offset = rng.random(1)*antenna.dt
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antenna.t = util.sampled_time(1/antenna.dt, start=0, end=antenna_timelength)
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antenna.t = util.sampled_time(1/antenna.dt, start=0, end=antenna_timelength)
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antenna.signal = interp1d_template(antenna.t - antenna.peak_time)
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antenna.signal = interp1d_template(antenna.t - antenna.peak_time)
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antenna.peak_sample = antenna.peak_time/antenna.dt
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antenna_true_signal = antenna.signal
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true_time_offset = antenna.peak_time - template.peak_time
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antenna.peak_sample = antenna.peak_time/antenna.dt
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antenna_true_signal = antenna.signal
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if do_plots:
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print(f"Antenna Peak Time: {antenna.peak_time}")
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print(f"Antenna Peak Sample: {antenna.peak_sample}")
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true_time_offset = antenna.peak_time - template.peak_time
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if False: # flip polarisation
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antenna.signal *= -1
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if False: # flip polarisation
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antenna.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.signal))
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filtered_noise = antenna_bp(noise_realisation, *bp_freq, antenna.dt)
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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.signal))
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filtered_noise = antenna_bp(noise_realisation, *bp_freq, antenna.dt)
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antenna.signal += filtered_noise
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antenna.signal += filtered_noise
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if do_plots: # 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', alpha=0.9)
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axs[0].plot(antenna.t, antenna.signal - filtered_noise, label='bandpassed w/o noise', alpha=0.9)
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axs[0].legend()
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if do_plots: # 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', alpha=0.9)
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axs[0].plot(antenna.t, antenna.signal - filtered_noise, label='bandpassed w/o noise', alpha=0.9)
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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='true moved orig')
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axs[1].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='true moved orig')
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axs[1].legend()
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axs[0].grid()
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axs[1].grid()
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axs[0].grid()
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axs[1].grid()
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fig.savefig('figures/11_antenna_signals.pdf')
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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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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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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 False:
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plt.close(fig)
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axs2 = None
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if True: # upsampled trace
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upsampled_trace, upsampled_t = trace_upsampler(antenna.signal, template.t, antenna.t)
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if do_plots: # 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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# restore
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axs[0].set_xlim(*old_xlims)
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if True:
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plt.close(fig2)
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plt.close(fig)
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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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axs2 = None
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if True: # upsampled trace
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upsampled_trace, upsampled_t = trace_upsampler(antenna.signal, template.t, antenna.t)
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else: # downsampled template
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raise NotImplementedError
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if do_plots: # 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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corrs, (out1_signal, out2_template, 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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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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# 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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time_residuals[j] = best_time_lag - true_time_offset
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fig2.savefig('figures/11_upsampled.pdf')
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if not do_plots:
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continue
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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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if do_plots and axs2:
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axs2[-1].axvline(best_time_lag, color='r', alpha=0.5, linewidth=2)
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axs2[-1].axvline(true_time_offset, color='g', alpha=0.5, linewidth=2)
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if True:
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plt.close(fig2)
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# Show the final signals correlated
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if do_plots:
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# amplitude scaling required for single axis plotting
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template_amp_scaler = max(abs(template.signal)) / max(abs(antenna.signal))
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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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# start the figure
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fig, axs = plt.subplots(2, 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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else: # downsampled template
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raise NotImplementedError
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offset_list = [
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[best_time_lag, dict(label=template.name, color='orange')],
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[true_time_offset, dict(label='True offset', color='green')],
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]
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corrs, (out1_signal, out2_template, 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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# Signal
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i=0
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axs[i].set_ylabel("Amplitude", **ylabel_kwargs)
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axs[i].plot(antenna.t, antenna.signal, label=antenna.name)
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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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time_residuals[j] = best_time_lag - true_time_offset
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# Plot the template
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for offset_args in offset_list:
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this_kwargs = offset_args[1]
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offset = offset_args[0]
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if not do_plots:
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continue
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l = axs[i].plot(offset + template.t, template_amp_scaler * template.signal, **this_kwargs)
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if do_plots and axs2:
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axs2[-1].axvline(best_time_lag, color='r', alpha=0.5, linewidth=2)
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axs2[-1].axvline(true_time_offset, color='g', alpha=0.5, linewidth=2)
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axs[i].legend()
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# Show the final signals correlated
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if do_plots:
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# amplitude scaling required for single axis plotting
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template_amp_scaler = max(abs(template.signal)) / max(abs(antenna.signal))
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# Correlation
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i=1
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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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# start the figure
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fig, axs = plt.subplots(2, 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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# Lines across both axes
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for offset_args in offset_list:
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this_kwargs = offset_args[1]
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offset = offset_args[0]
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for i in [0,1]:
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axs[i].axvline(offset, ls='--', color=this_kwargs['color'], alpha=0.7)
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axs[0].axvline(offset + len(template.signal) * (template.t[1] - template.t[0]), color=this_kwargs['color'], alpha=0.7)
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if True: # zoom
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wx = len(template.signal) * (template.dt)/2
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t0 = best_time_lag
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old_xlims = axs[0].get_xlim()
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axs[i].set_xlim( x0-wx, x0+3*wx)
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fig.savefig('figures/11_corrs_zoom.pdf')
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# restore
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axs[i].set_xlim(*old_xlims)
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fig.tight_layout()
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fig.savefig('figures/11_corrs.pdf')
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if False:
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plt.close(fig)
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# Make a plot of the time residuals
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if len(time_residuals) > 1:
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hist_kwargs = dict(bins='sqrt', density=False, alpha=0.8, histtype='step')
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fig, ax = plt.subplots()
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ax.set_title(
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"Template Correlation Lag finding"
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+ f"\n template dt: {template.dt*1e3: .1e}ps"
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+ f"; antenna dt: {antenna.dt: .1e}ns"
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+ f"; noise_factor: {noise_sigma_factor: .1e}"
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)
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ax.set_xlabel("Time Residual [ns]")
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ax.set_ylabel("#")
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counts, bins, _patches = ax.hist(time_residuals, **hist_kwargs)
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if True: # fit gaussian to histogram
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min_x = min(time_residuals)
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max_x = max(time_residuals)
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dx = bins[1] - bins[0]
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scale = len(time_residuals) * dx
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xs = np.linspace(min_x, max_x)
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# do the fit
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name = "Norm"
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param_names = [ "$\\mu$", "$\\sigma$" ]
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distr_func = stats.norm
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label = name +"(" + ','.join(param_names) + ')'
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# plot
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fit_params = distr_func.fit(time_residuals)
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fit_ys = scale * distr_func.pdf(xs, *fit_params)
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ax.plot(xs, fit_ys, label=label)
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# chisq
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ct = np.diff(distr_func.cdf(bins, *fit_params))*np.sum(counts)
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if True:
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ct *= np.sum(counts)/np.sum(ct)
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c2t = stats.chisquare(counts, ct, ddof=len(fit_params))
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chisq_strs = [
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f"$\\chi^2$/dof = {c2t[0]: .2g}/{len(fit_params)}"
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offset_list = [
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[best_time_lag, dict(label=template.name, color='orange')],
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[true_time_offset, dict(label='True offset', color='green')],
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]
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# text on plot
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text_str = "\n".join(
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[label]
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+
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[ f"{param} = {value: .2e}" for param, value in zip_longest(param_names, fit_params, fillvalue='?') ]
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+
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chisq_strs
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)
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# Signal
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i=0
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axs[i].set_ylabel("Amplitude", **ylabel_kwargs)
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axs[i].plot(antenna.t, antenna.signal, label=antenna.name)
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ax.text( *(0.02, 0.95), text_str, fontsize=12, ha='left', va='top', transform=ax.transAxes)
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# Plot the template
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for offset_args in offset_list:
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this_kwargs = offset_args[1]
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offset = offset_args[0]
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fig.savefig("figures/11_time_residual_hist.pdf")
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l = axs[i].plot(offset + template.t, template_amp_scaler * template.signal, **this_kwargs)
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axs[i].legend()
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# Correlation
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i=1
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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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# Lines across both axes
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for offset_args in offset_list:
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this_kwargs = offset_args[1]
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offset = offset_args[0]
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for i in [0,1]:
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axs[i].axvline(offset, ls='--', color=this_kwargs['color'], alpha=0.7)
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axs[0].axvline(offset + len(template.signal) * (template.t[1] - template.t[0]), color=this_kwargs['color'], alpha=0.7)
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if True: # zoom
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wx = len(template.signal) * (template.dt)/2
|
||||
t0 = best_time_lag
|
||||
|
||||
old_xlims = axs[0].get_xlim()
|
||||
axs[i].set_xlim( x0-wx, x0+3*wx)
|
||||
fig.savefig('figures/11_corrs_zoom.pdf')
|
||||
|
||||
# restore
|
||||
axs[i].set_xlim(*old_xlims)
|
||||
|
||||
fig.tight_layout()
|
||||
fig.savefig('figures/11_corrs.pdf')
|
||||
|
||||
if True:
|
||||
plt.close(fig)
|
||||
|
||||
print()# separating tqdm
|
||||
# Make a plot of the time residuals
|
||||
if len(time_residuals) > 1:
|
||||
time_accuracies[k] = np.std(time_residuals)
|
||||
|
||||
hist_kwargs = dict(bins='sqrt', density=False, alpha=0.8, histtype='step')
|
||||
fig, ax = plt.subplots()
|
||||
ax.set_title(
|
||||
"Template Correlation Lag finding"
|
||||
+ f"\n template dt: {template.dt*1e3: .1e}ps"
|
||||
+ f"; antenna dt: {antenna.dt: .1e}ns"
|
||||
+ f"; noise_factor: {noise_sigma_factor: .1e}"
|
||||
)
|
||||
ax.set_xlabel("Time Residual [ns]")
|
||||
ax.set_ylabel("#")
|
||||
|
||||
counts, bins, _patches = ax.hist(time_residuals, **hist_kwargs)
|
||||
if True: # fit gaussian to histogram
|
||||
min_x = min(time_residuals)
|
||||
max_x = max(time_residuals)
|
||||
|
||||
dx = bins[1] - bins[0]
|
||||
scale = len(time_residuals) * dx
|
||||
|
||||
xs = np.linspace(min_x, max_x)
|
||||
|
||||
# do the fit
|
||||
name = "Norm"
|
||||
param_names = [ "$\\mu$", "$\\sigma$" ]
|
||||
distr_func = stats.norm
|
||||
|
||||
label = name +"(" + ','.join(param_names) + ')'
|
||||
|
||||
# plot
|
||||
fit_params = distr_func.fit(time_residuals)
|
||||
fit_ys = scale * distr_func.pdf(xs, *fit_params)
|
||||
ax.plot(xs, fit_ys, label=label)
|
||||
|
||||
# chisq
|
||||
ct = np.diff(distr_func.cdf(bins, *fit_params))*np.sum(counts)
|
||||
if True:
|
||||
ct *= np.sum(counts)/np.sum(ct)
|
||||
c2t = stats.chisquare(counts, ct, ddof=len(fit_params))
|
||||
chisq_strs = [
|
||||
f"$\\chi^2$/dof = {c2t[0]: .2g}/{len(fit_params)}"
|
||||
]
|
||||
|
||||
# text on plot
|
||||
text_str = "\n".join(
|
||||
[label]
|
||||
+
|
||||
[ f"{param} = {value: .2e}" for param, value in zip_longest(param_names, fit_params, fillvalue='?') ]
|
||||
+
|
||||
chisq_strs
|
||||
)
|
||||
|
||||
ax.text( *(0.02, 0.95), text_str, fontsize=12, ha='left', va='top', transform=ax.transAxes)
|
||||
|
||||
fig.savefig("figures/11_time_residual_hist_{noise_sigma_factor: .1e}.pdf")
|
||||
|
||||
if True:
|
||||
plt.close(fig)
|
||||
|
||||
# SNR time accuracy plot
|
||||
if True:
|
||||
fig, ax = plt.subplots()
|
||||
ax.set_title("Template matching SNR vs time accuracy")
|
||||
ax.set_xlabel("Signal to Noise Factor")
|
||||
ax.set_ylabel("Time Accuracy [ns]")
|
||||
|
||||
if True:
|
||||
ax.set_xscale('log')
|
||||
ax.set_yscale('log')
|
||||
|
||||
# plot the values
|
||||
ax.plot(1/np.asarray(noise_factors), time_accuracies, ls='none', marker='o')
|
||||
|
||||
|
||||
# Set horizontal line at 1 ns
|
||||
if True:
|
||||
ax.axhline(1, ls='--', alpha=0.8, color='g')
|
||||
ax.grid()
|
||||
|
||||
fig.tight_layout()
|
||||
fig.savefig("figures/11_time_res_vs_snr.pdf")
|
||||
|
||||
plt.show()
|
||||
|
|
|
|||
Loading…
Reference in a new issue