mirror of
https://gitlab.science.ru.nl/mthesis-edeboone/m-thesis-introduction.git
synced 2024-11-14 10:33:32 +01:00
249 lines
8.1 KiB
Python
249 lines
8.1 KiB
Python
"""
|
|
Routines needed to analyse a beacon signal
|
|
"""
|
|
import numpy as np
|
|
from scipy import signal
|
|
|
|
# monkey patch correlation_lags into signal if it does not exist
|
|
if not hasattr(signal, 'correlation_lags'):
|
|
def correlation_lags(in1_len, in2_len, mode='full'):
|
|
r"""
|
|
Calculates the lag / displacement indices array for 1D cross-correlation.
|
|
Parameters
|
|
----------
|
|
in1_size : int
|
|
First input size.
|
|
in2_size : int
|
|
Second input size.
|
|
mode : str {'full', 'valid', 'same'}, optional
|
|
A string indicating the size of the output.
|
|
See the documentation `correlate` for more information.
|
|
See Also
|
|
--------
|
|
correlate : Compute the N-dimensional cross-correlation.
|
|
Returns
|
|
-------
|
|
lags : array
|
|
Returns an array containing cross-correlation lag/displacement indices.
|
|
Indices can be indexed with the np.argmax of the correlation to return
|
|
the lag/displacement.
|
|
Notes
|
|
-----
|
|
Cross-correlation for continuous functions :math:`f` and :math:`g` is
|
|
defined as:
|
|
.. math::
|
|
\left ( f\star g \right )\left ( \tau \right )
|
|
\triangleq \int_{t_0}^{t_0 +T}
|
|
\overline{f\left ( t \right )}g\left ( t+\tau \right )dt
|
|
Where :math:`\tau` is defined as the displacement, also known as the lag.
|
|
Cross correlation for discrete functions :math:`f` and :math:`g` is
|
|
defined as:
|
|
.. math::
|
|
\left ( f\star g \right )\left [ n \right ]
|
|
\triangleq \sum_{-\infty}^{\infty}
|
|
\overline{f\left [ m \right ]}g\left [ m+n \right ]
|
|
Where :math:`n` is the lag.
|
|
Examples
|
|
--------
|
|
Cross-correlation of a signal with its time-delayed self.
|
|
>>> from scipy import signal
|
|
>>> from numpy.random import default_rng
|
|
>>> rng = default_rng()
|
|
>>> x = rng.standard_normal(1000)
|
|
>>> y = np.concatenate([rng.standard_normal(100), x])
|
|
>>> correlation = signal.correlate(x, y, mode="full")
|
|
>>> lags = signal.correlation_lags(x.size, y.size, mode="full")
|
|
>>> lag = lags[np.argmax(correlation)]
|
|
"""
|
|
|
|
# calculate lag ranges in different modes of operation
|
|
if mode == "full":
|
|
# the output is the full discrete linear convolution
|
|
# of the inputs. (Default)
|
|
lags = np.arange(-in2_len + 1, in1_len)
|
|
elif mode == "same":
|
|
# the output is the same size as `in1`, centered
|
|
# with respect to the 'full' output.
|
|
# calculate the full output
|
|
lags = np.arange(-in2_len + 1, in1_len)
|
|
# determine the midpoint in the full output
|
|
mid = lags.size // 2
|
|
# determine lag_bound to be used with respect
|
|
# to the midpoint
|
|
lag_bound = in1_len // 2
|
|
# calculate lag ranges for even and odd scenarios
|
|
if in1_len % 2 == 0:
|
|
lags = lags[(mid-lag_bound):(mid+lag_bound)]
|
|
else:
|
|
lags = lags[(mid-lag_bound):(mid+lag_bound)+1]
|
|
elif mode == "valid":
|
|
# the output consists only of those elements that do not
|
|
# rely on the zero-padding. In 'valid' mode, either `in1` or `in2`
|
|
# must be at least as large as the other in every dimension.
|
|
|
|
# the lag_bound will be either negative or positive
|
|
# this let's us infer how to present the lag range
|
|
lag_bound = in1_len - in2_len
|
|
if lag_bound >= 0:
|
|
lags = np.arange(lag_bound + 1)
|
|
else:
|
|
lags = np.arange(lag_bound, 1)
|
|
return lags
|
|
|
|
signal.correlation_lags = correlation_lags
|
|
|
|
##### end of monkey patch correlation_lags
|
|
|
|
def beacon_time_delay(samplerate, ref_beacon, beacon):
|
|
"""
|
|
Determine the time delay between two beacons using correlation.
|
|
|
|
"""
|
|
grid = correlation_grid(in1_len=len(ref_beacon), in2_len=len(beacon), mode='full')
|
|
time_lag, errs = lag_gridsearch(grid, samplerate, ref_beacon, beacon)
|
|
|
|
return time_lag, errs
|
|
|
|
def beacon_phase_delay(samplerate, f_beacon, ref_beacon, beacon):
|
|
"""
|
|
Determine total phase delay between two beacons using correlation.
|
|
|
|
Internally uses beacon_time_delay.
|
|
"""
|
|
time_delay, errs = beacon_time_delay(samplerate, ref_beacon, beacon)
|
|
|
|
phase = 2*np.pi*f_beacon*time_delay
|
|
phase_err = 2*np.pi*f_beacon*errs
|
|
|
|
return phase, phase_err
|
|
|
|
def beacon_integer_period(samplerate, f_beacon, ref_impulse, impulse, k_step=1):
|
|
return _beacon_integer_period_sum(samplerate, f_beacon, ref_impulse, impulse, k_step=k_step)
|
|
|
|
def _beacon_integer_period_sum(samplerate, f_beacon, ref_impulse, impulse, k_step=1):
|
|
"""
|
|
Use the maximum of a coherent sum to determine
|
|
the best number of periods of f_beacon.
|
|
"""
|
|
max_k = int( len(ref_impulse)*f_beacon/samplerate )
|
|
ks = np.arange(0, max_k, step=k_step)
|
|
|
|
maxima = np.empty(len(ks))
|
|
|
|
best_i = 0
|
|
|
|
for i,k in enumerate(ks, 0):
|
|
augmented_impulse = util.time_roll(impulse, samplerate, k/f_beacon)
|
|
|
|
maxima[i] = max(ref_impulse + augmented_impulse)
|
|
|
|
if maxima[i] > maxima[best_i]:
|
|
best_i = i
|
|
|
|
return ks[best_i], (ks, maxima)
|
|
|
|
|
|
def lag_gridsearch(grid, sample_rate, reference, signal_data):
|
|
"""
|
|
Return the best time shift found when doing a grid search.
|
|
|
|
Parameters
|
|
----------
|
|
lag_grid - ndarray
|
|
The array specifying the grid that is to be searched.
|
|
sample_rate - float
|
|
Sample rate of signal_data to transform index to time.
|
|
signal_data - ndarray
|
|
The real signal to find the time shift for.
|
|
reference - ndarray
|
|
Real signal to use as reference to obtain lag.
|
|
|
|
Returns
|
|
-------
|
|
lag : ndarray
|
|
The best time shift obtained
|
|
err : tuple
|
|
Difference to the previous and next time shift from lag, resp.
|
|
"""
|
|
|
|
assert signal_data.shape >= reference.shape, str(signal_data.shape) + " " + str(reference.shape)
|
|
|
|
corrs = grid_correlate(grid, reference, signal_data)
|
|
|
|
idx = np.argmax(corrs)
|
|
|
|
lag = grid[idx]/sample_rate
|
|
|
|
err_min = (grid[idx-1]-grid[idx])/(2*sample_rate)
|
|
err_plus = (grid[idx+1]-grid[idx])/(2*sample_rate)
|
|
|
|
return lag, np.array([err_min, err_plus])
|
|
|
|
|
|
def grid_correlate(grid, reference, x):
|
|
"""
|
|
Determine correlation between x and reference using grid as
|
|
the lags to be used for the correlation.
|
|
|
|
Parameters
|
|
----------
|
|
grid - ndarray
|
|
The array specifying the grid that is to be searched.
|
|
x - ndarray
|
|
The real signal to find the time shift for.
|
|
reference - ndarray
|
|
Real signal to use as reference to obtain lag.
|
|
|
|
Returns
|
|
-------
|
|
corrs - ndarray
|
|
The correlations along grid.
|
|
"""
|
|
grid = np.asarray(grid)
|
|
x = np.asarray(x)
|
|
reference = np.asarray(reference)
|
|
|
|
assert x.shape >= reference.shape, str(signal_data.shape) + " " + str(reference.shape)
|
|
|
|
reference = np.pad(reference, (0,len(x)-len(reference)), 'constant', constant_values=0)
|
|
|
|
ref_conj = np.conjugate(reference)
|
|
|
|
corrs = np.array([np.dot(np.roll(ref_conj, lag), x) for lag in grid], dtype=np.float64)
|
|
|
|
return corrs
|
|
|
|
def correlation_grid(grid_size=None, in1_len=None, in2_len = None, end = None, start=None, mode='full'):
|
|
"""
|
|
Abuse correlation_lags to determine the endpoints of the grid.
|
|
"""
|
|
|
|
if in1_len is not None or in2_len is not None:
|
|
if in2_len is None:
|
|
in2_len = in1_len
|
|
elif in1_len is None:
|
|
in1_len = in2_len
|
|
|
|
lags = signal.correlation_lags(in1_len, in2_len, mode=mode)
|
|
|
|
max_lag = max(lags)
|
|
min_lag = min(lags)
|
|
else:
|
|
max_lag = np.inf
|
|
min_lag = -np.inf
|
|
|
|
if end is None:
|
|
end = max_lag
|
|
elif end > max_lag:
|
|
raise ValueError("Grid end is too high")
|
|
|
|
if start is None:
|
|
start = min_lag
|
|
elif start < min_lag:
|
|
raise ValueError("Grid start is too low")
|
|
|
|
if grid_size is None:
|
|
grid_size = end - start
|
|
|
|
return np.linspace(start, end, grid_size, dtype=int, endpoint=False)
|
|
|