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222 lines
6.9 KiB
Python
222 lines
6.9 KiB
Python
#!/usr/bin/env python3
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"""
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Define the TravelSignal class.
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"""
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import numpy as np
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import scipy.interpolate as interp
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class TravelSignal:
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"""
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Model an arbitrary digitised signal that can be translated to another position and time.
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"""
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def __init__(self, signal, sample_rate, t_0 = 0, x_0 = 0, periodic=True, interp1d_kw = None, velocity=None):
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"""
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Initialise by saving the raw signal
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Parameters
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----------
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signal : arraylike
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The raw signal to wrap.
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sample_rate : float
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Sample rate of the raw signal.
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t_0 : float, optional
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Time that this signal is sent out.
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x_0 : float, optional
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Location that this signal is sent out from.
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periodic : bool, optional
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Translated signal is 0 if it is not periodic
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and the time/distance is outside the samples.
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interp1d_kw : bool or dict, optional
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Use scipy.interpolate's interp1d_kw for interpolation.
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Set to True, or a dictionary to enable.
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Dictionary will be entered in as **kwargs.
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velocity : float, optional
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Defaults to the speed of light in m/s.
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"""
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self.raw = np.asarray(signal)
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self.periodic = periodic
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self.sample_rate = sample_rate # Hz
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self.sample_length = len(self.raw)
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self.time_length = self.sample_length*sample_rate # s
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self.velocity = 299792458 if velocity is None else velocity # m / s
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self.x_0 = x_0 # m
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self.t_0 = t_0 # s
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# choose interpolation method
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if not interp1d_kw:
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self.interp_f = None
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# offload interpolation to scipy.interpolate
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else:
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interp1d_kw_defaults = {
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"copy": False,
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"kind": 'linear',
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"assume_sorted": True,
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"bounds_error": True
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}
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if self.periodic:
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interp1d_kw_defaults['bounds_error'] = False
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interp1d_kw_defaults['fill_value'] = (self.raw[-1], self.raw[0])
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# merge kwargs
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if interp1d_kw is not True:
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interp1d_kw = { **interp1d_kw_defaults, **interp1d_kw }
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self.interp_f = interp.interp1d(
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np.arange(0, self.sample_length),
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self.raw,
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**interp1d_kw
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)
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def __len__(self):
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return self.sample_length
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def __call__(self, t_f = None, x_f = None, **kwargs):
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"""
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Allow this class to be used as a function.
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"""
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return self._translate(t_f, x_f, **kwargs)[0]
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def _translate(self, t_f = None, x_f = None, t_0 = None, x_0 = None, velocity = None):
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"""
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Translate the signal from (t_0, x_0) to (t_f, x_f) with optional velocity.
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Returns the signal at (t_f, x_f)
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"""
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total_time_offset = self.total_time_offset(t_f=t_f, x_f=x_f, t_0=t_0, x_0=x_0, velocity=velocity)
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n_offset = (total_time_offset * self.sample_rate )
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# periodic signal
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if self.periodic:
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n_offset = n_offset % self.sample_length
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# non-periodic and possibly outside the bounds
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else:
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# this is a numpy array
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if hasattr(n_offset, 'ndim') and n_offset.ndim > 0:
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mask_idx = np.nonzero( (0 > n_offset) | (n_offset >= self.sample_length) )
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n_offset[mask_idx] = 0
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# not a numpy array
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else:
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# outside the bounds
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if 0 > n_offset or n_offset > self.sample_length:
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n_offset = np.nan
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# n_offset is invalid
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# set amplitude to zero
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if n_offset is np.nan:
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amplitude = 0
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# n_offset is valid, interpolate the amplitude
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else:
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# offload to scipy interpolation
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if self.interp_f:
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amplitude = self.interp_f(n_offset)
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# self written linear interpolation
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else:
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n_offset = np.asarray(n_offset)
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n_offset_eps, n_offset_int = np.modf(n_offset)
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n_offset_int = n_offset.astype(int)
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if True:
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amplitude = (1-n_offset_eps) * self.raw[n_offset_int] \
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+ n_offset_eps * self.raw[(n_offset_int + 1) % self.sample_length]
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# use nearest value instead of interpolation
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else:
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amplitude = self.raw[n_offset_int]
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if not self.periodic:
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if hasattr(amplitude, 'ndim'):
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amplitude[mask_idx] = 0
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return amplitude, total_time_offset
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def spatial_time(self, x_f, velocity=None, x_0=None):
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"""
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Calculate the time offset caused by a spatial difference.
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"""
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if velocity is None:
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velocity = self.velocity
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if x_0 is None:
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x_0 = self.x_0
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return np.sum(np.sqrt( (x_f - x_0)**2 )/velocity)
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def total_time_offset(self, t_f = None, x_f = None, t_0 = None, x_0 = None, velocity = None):
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"""
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Calculate how much time shifting is needed to go from (t_0, x_0) to (t_f, x_f).
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Convention:
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(t_0, x_0) < (t_f, x_0) gives a positive time shift,
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(t_0, x_0) != (t_0, x_f) gives a negative time shift
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Returns:
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the time shift
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"""
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## spatial offset
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if x_f is None:
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spatial_time_offset = 0
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else:
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x_f = np.asarray(x_f)
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if x_0 is None:
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x_0 = self.x_0
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spatial_time_offset = self.spatial_time(x_f, x_0=x_0, velocity=velocity)
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## temporal offset
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if t_f is None:
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temporal_time_offset = 0
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else:
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t_f = np.asarray(t_f)
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if t_0 is None:
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t_0 = self.t_0
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temporal_time_offset = t_f - t_0
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return temporal_time_offset - spatial_time_offset
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if __name__ == "__main__":
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import matplotlib.pyplot as plt
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from scipy.stats import norm
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sample_rate = 3e2 # Hz
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t_offset = 8
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periodic = False
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time = t_offset + np.arange(0, 1, 1/sample_rate) #s
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time2 = t_offset + np.arange(-1.5, 1, 1/sample_rate) #s
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signal = norm.pdf(time, time[len(time)//2], (time[-1] - time[0])/10)
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mysignal = TravelSignal(signal, sample_rate, t_0 = t_offset, periodic=True)
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mysignal2 = TravelSignal(signal, sample_rate, t_0 = t_offset, periodic=False)
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fig, ax = plt.subplots(1, 1, figsize=(16,4))
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ax.set_title("Raw and TravelSignal")
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ax.set_ylabel("Amplitude")
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ax.set_xlabel("Time")
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ax.plot(time, signal, label='Raw signal')
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ax.plot(time2, mysignal(time2) +0.5, '.-', label='TravelSignal(periodic)+0.5')
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ax.plot(time2, mysignal2(time2)-0.5, '.-', label='TravelSignal-0.5')
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ax.legend()
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plt.show();
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