Simu: 8.1 Move beacon delay code into lib
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from . import signals
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from . import location
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from . import sampling
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from .plotting import *
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from .util import *
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"""
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Routines needed to analyse a beacon signal
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"""
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import numpy as np
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from scipy import signal
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# monkey patch correlation_lags into signal if it does not exist
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if not hasattr(signal, 'correlation_lags'):
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def correlation_lags(in1_len, in2_len, mode='full'):
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r"""
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Calculates the lag / displacement indices array for 1D cross-correlation.
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Parameters
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----------
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in1_size : int
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First input size.
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in2_size : int
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Second input size.
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mode : str {'full', 'valid', 'same'}, optional
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A string indicating the size of the output.
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See the documentation `correlate` for more information.
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See Also
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--------
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correlate : Compute the N-dimensional cross-correlation.
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Returns
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-------
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lags : array
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Returns an array containing cross-correlation lag/displacement indices.
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Indices can be indexed with the np.argmax of the correlation to return
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the lag/displacement.
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Notes
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-----
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Cross-correlation for continuous functions :math:`f` and :math:`g` is
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defined as:
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.. math::
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\left ( f\star g \right )\left ( \tau \right )
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\triangleq \int_{t_0}^{t_0 +T}
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\overline{f\left ( t \right )}g\left ( t+\tau \right )dt
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Where :math:`\tau` is defined as the displacement, also known as the lag.
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Cross correlation for discrete functions :math:`f` and :math:`g` is
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defined as:
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.. math::
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\left ( f\star g \right )\left [ n \right ]
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\triangleq \sum_{-\infty}^{\infty}
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\overline{f\left [ m \right ]}g\left [ m+n \right ]
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Where :math:`n` is the lag.
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Examples
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--------
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Cross-correlation of a signal with its time-delayed self.
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>>> from scipy import signal
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>>> from numpy.random import default_rng
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>>> rng = default_rng()
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>>> x = rng.standard_normal(1000)
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>>> y = np.concatenate([rng.standard_normal(100), x])
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>>> correlation = signal.correlate(x, y, mode="full")
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>>> lags = signal.correlation_lags(x.size, y.size, mode="full")
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>>> lag = lags[np.argmax(correlation)]
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"""
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# calculate lag ranges in different modes of operation
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if mode == "full":
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# the output is the full discrete linear convolution
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# of the inputs. (Default)
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lags = np.arange(-in2_len + 1, in1_len)
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elif mode == "same":
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# the output is the same size as `in1`, centered
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# with respect to the 'full' output.
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# calculate the full output
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lags = np.arange(-in2_len + 1, in1_len)
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# determine the midpoint in the full output
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mid = lags.size // 2
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# determine lag_bound to be used with respect
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# to the midpoint
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lag_bound = in1_len // 2
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# calculate lag ranges for even and odd scenarios
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if in1_len % 2 == 0:
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lags = lags[(mid-lag_bound):(mid+lag_bound)]
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else:
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lags = lags[(mid-lag_bound):(mid+lag_bound)+1]
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elif mode == "valid":
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# the output consists only of those elements that do not
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# rely on the zero-padding. In 'valid' mode, either `in1` or `in2`
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# must be at least as large as the other in every dimension.
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# the lag_bound will be either negative or positive
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# this let's us infer how to present the lag range
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lag_bound = in1_len - in2_len
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if lag_bound >= 0:
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lags = np.arange(lag_bound + 1)
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else:
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lags = np.arange(lag_bound, 1)
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return lags
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signal.correlation_lags = correlation_lags
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##### end of monkey patch correlation_lags
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def beacon_time_delay(samplerate, ref_beacon, beacon):
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grid = correlation_grid(in1_len=len(ref_beacon), in2_len=len(beacon), mode='full')
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time_lag, errs = lag_gridsearch(grid, samplerate, ref_beacon, beacon)
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return time_lag, errs
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def beacon_phase_delay(samplerate, f_beacon, ref_beacon, beacon):
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time_delay, errs = beacon_time_delay(samplerate, ref_beacon, beacon)
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phase = 2*np.pi*f_beacon*time_delay
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phase_err = 2*np.pi*f_beacon*errs
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return phase, phase_err
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def lag_gridsearch(grid, sample_rate, reference, signal_data):
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"""
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Return the best time shift found when doing a grid search.
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Parameters
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----------
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lag_grid - ndarray
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The array specifying the grid that is to be searched.
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sample_rate - float
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Sample rate of signal_data to transform index to time.
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signal_data - ndarray
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The real signal to find the time shift for.
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reference - ndarray
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Real signal to use as reference to obtain lag.
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Returns
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-------
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lag : ndarray
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The best time shift obtained
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err : tuple
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Difference to the previous and next time shift from lag, resp.
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"""
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assert signal_data.shape >= reference.shape, str(signal_data.shape) + " " + str(reference.shape)
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corrs = grid_correlate(grid, reference, signal_data)
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idx = np.argmax(corrs)
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lag = grid[idx]/sample_rate
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err_min = (grid[idx-1]-grid[idx])/(2*sample_rate)
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err_plus = (grid[idx+1]-grid[idx])/(2*sample_rate)
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return lag, np.array([err_min, err_plus])
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def grid_correlate(grid, reference, x):
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"""
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Determine correlation between x and reference using grid as
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the lags to be used for the correlation.
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Parameters
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----------
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grid - ndarray
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The array specifying the grid that is to be searched.
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x - ndarray
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The real signal to find the time shift for.
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reference - ndarray
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Real signal to use as reference to obtain lag.
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Returns
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-------
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corrs - ndarray
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The correlations along grid.
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"""
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grid = np.asarray(grid)
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x = np.asarray(x)
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reference = np.asarray(reference)
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assert x.shape >= reference.shape, str(signal_data.shape) + " " + str(reference.shape)
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reference = np.pad(reference, (0,len(x)-len(reference)), 'constant', constant_values=0)
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ref_conj = np.conjugate(reference)
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corrs = np.array([np.dot(np.roll(ref_conj, lag), x) for lag in grid], dtype=np.float64)
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return corrs
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def correlation_grid(grid_size=None, in1_len=None, in2_len = None, end = None, start=None, mode='full'):
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"""
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Abuse correlation_lags to determine the endpoints of the grid.
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"""
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if in1_len is not None or in2_len is not None:
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if in2_len is None:
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in2_len = in1_len
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elif in1_len is None:
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in1_len = in2_len
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lags = signal.correlation_lags(in1_len, in2_len, mode=mode)
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max_lag = max(lags)
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min_lag = min(lags)
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else:
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max_lag = np.inf
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min_lag = -np.inf
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if end is None:
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end = max_lag
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elif end > max_lag:
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raise ValueError("Grid end is too high")
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if start is None:
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start = min_lag
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elif start < min_lag:
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raise ValueError("Grid start is too low")
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if grid_size is None:
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grid_size = end - start
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return np.linspace(start, end, grid_size, dtype=int, endpoint=False)
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@ -24,205 +24,7 @@
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"sys.path.append(os.path.dirname(os.path.abspath(os.getcwd())))\n",
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"from lib.util import *\n",
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"\n",
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"\n",
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"# monkey patch correlation_lags into signal if it does not exist\n",
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"if not hasattr(signal, 'correlation_lags'):\n",
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" def correlation_lags(in1_len, in2_len, mode='full'):\n",
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" r\"\"\"\n",
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" Calculates the lag / displacement indices array for 1D cross-correlation.\n",
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" Parameters\n",
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" ----------\n",
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" in1_size : int\n",
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" First input size.\n",
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" in2_size : int\n",
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" Second input size.\n",
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" mode : str {'full', 'valid', 'same'}, optional\n",
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" A string indicating the size of the output.\n",
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" See the documentation `correlate` for more information.\n",
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" See Also\n",
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" --------\n",
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" correlate : Compute the N-dimensional cross-correlation.\n",
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" Returns\n",
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" -------\n",
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" lags : array\n",
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" Returns an array containing cross-correlation lag/displacement indices.\n",
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" Indices can be indexed with the np.argmax of the correlation to return\n",
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" the lag/displacement.\n",
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" Notes\n",
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" -----\n",
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" Cross-correlation for continuous functions :math:`f` and :math:`g` is\n",
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" defined as:\n",
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" .. math::\n",
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" \\left ( f\\star g \\right )\\left ( \\tau \\right )\n",
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" \\triangleq \\int_{t_0}^{t_0 +T}\n",
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" \\overline{f\\left ( t \\right )}g\\left ( t+\\tau \\right )dt\n",
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" Where :math:`\\tau` is defined as the displacement, also known as the lag.\n",
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" Cross correlation for discrete functions :math:`f` and :math:`g` is\n",
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" defined as:\n",
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" .. math::\n",
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" \\left ( f\\star g \\right )\\left [ n \\right ]\n",
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" \\triangleq \\sum_{-\\infty}^{\\infty}\n",
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" \\overline{f\\left [ m \\right ]}g\\left [ m+n \\right ]\n",
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" Where :math:`n` is the lag.\n",
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" Examples\n",
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" --------\n",
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" Cross-correlation of a signal with its time-delayed self.\n",
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" >>> from scipy import signal\n",
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" >>> from numpy.random import default_rng\n",
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" >>> rng = default_rng()\n",
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" >>> x = rng.standard_normal(1000)\n",
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" >>> y = np.concatenate([rng.standard_normal(100), x])\n",
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" >>> correlation = signal.correlate(x, y, mode=\"full\")\n",
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" >>> lags = signal.correlation_lags(x.size, y.size, mode=\"full\")\n",
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" >>> lag = lags[np.argmax(correlation)]\n",
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" \"\"\"\n",
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"\n",
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" # calculate lag ranges in different modes of operation\n",
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" if mode == \"full\":\n",
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" # the output is the full discrete linear convolution\n",
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" # of the inputs. (Default)\n",
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" lags = np.arange(-in2_len + 1, in1_len)\n",
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" elif mode == \"same\":\n",
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" # the output is the same size as `in1`, centered\n",
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" # with respect to the 'full' output.\n",
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" # calculate the full output\n",
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" lags = np.arange(-in2_len + 1, in1_len)\n",
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" # determine the midpoint in the full output\n",
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" mid = lags.size // 2\n",
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" # determine lag_bound to be used with respect\n",
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" # to the midpoint\n",
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" lag_bound = in1_len // 2\n",
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" # calculate lag ranges for even and odd scenarios\n",
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" if in1_len % 2 == 0:\n",
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" lags = lags[(mid-lag_bound):(mid+lag_bound)]\n",
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" else:\n",
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" lags = lags[(mid-lag_bound):(mid+lag_bound)+1]\n",
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" elif mode == \"valid\":\n",
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" # the output consists only of those elements that do not\n",
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" # rely on the zero-padding. In 'valid' mode, either `in1` or `in2`\n",
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" # must be at least as large as the other in every dimension.\n",
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"\n",
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" # the lag_bound will be either negative or positive\n",
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" # this let's us infer how to present the lag range\n",
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" lag_bound = in1_len - in2_len\n",
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" if lag_bound >= 0:\n",
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" lags = np.arange(lag_bound + 1)\n",
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" else:\n",
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" lags = np.arange(lag_bound, 1)\n",
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" return lags\n",
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"\n",
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" signal.correlation_lags = correlation_lags"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"def lag_gridsearch(grid, sample_rate, reference, signal_data):\n",
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" \"\"\"\n",
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" Return the best time shift found when doing a grid search.\n",
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" \n",
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" Parameters\n",
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" ----------\n",
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" lag_grid - ndarray\n",
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" The array specifying the grid that is to be searched.\n",
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" sample_rate - float\n",
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" Sample rate of signal_data to transform index to time.\n",
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" signal_data - ndarray\n",
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" The real signal to find the time shift for.\n",
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" reference - ndarray\n",
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" Real signal to use as reference to obtain lag.\n",
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" \n",
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" Returns\n",
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" -------\n",
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" lag : ndarray\n",
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" The best time shift obtained\n",
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" err : tuple\n",
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" Difference to the previous and next time shift from lag, resp.\n",
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" \"\"\"\n",
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"\n",
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" assert signal_data.shape >= reference.shape, str(signal_data.shape) + \" \" + str(reference.shape)\n",
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" \n",
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" corrs = grid_correlate(grid, reference, signal_data)\n",
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" \n",
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" idx = np.argmax(corrs)\n",
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"\n",
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" lag = grid[idx]/sample_rate\n",
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" \n",
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" err_min = (grid[idx-1]-grid[idx])/(2*sample_rate)\n",
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" err_plus = (grid[idx+1]-grid[idx])/(2*sample_rate)\n",
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"\n",
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" return lag, np.array([err_min, err_plus])\n",
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" \n",
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"\n",
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"def grid_correlate(grid, reference, x):\n",
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" \"\"\"\n",
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" Determine correlation between x and reference using grid as \n",
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" the lags to be used for the correlation.\n",
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" \n",
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" Parameters\n",
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" ----------\n",
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" grid - ndarray\n",
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" The array specifying the grid that is to be searched.\n",
|
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" x - ndarray\n",
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" The real signal to find the time shift for.\n",
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" reference - ndarray\n",
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" Real signal to use as reference to obtain lag.\n",
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" \n",
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" Returns\n",
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" -------\n",
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" corrs - ndarray\n",
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" The correlations along grid.\n",
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" \"\"\"\n",
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" grid = np.asarray(grid)\n",
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" x = np.asarray(x)\n",
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" reference = np.asarray(reference)\n",
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"\n",
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" assert x.shape >= reference.shape, str(signal_data.shape) + \" \" + str(reference.shape)\n",
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" \n",
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" reference = np.pad(reference, (0,len(x)-len(reference)), 'constant', constant_values=0)\n",
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" \n",
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" ref_conj = np.conjugate(reference)\n",
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" \n",
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" corrs = np.array([np.dot(np.roll(ref_conj, lag), x) for lag in grid], dtype=np.float64)\n",
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" \n",
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" return corrs\n",
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"\n",
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"def correlation_grid(grid_size=None, in1_len=None, in2_len = None, end = None, start=None, mode='full'):\n",
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" \"\"\"\n",
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" Abuse correlation_lags to determine the endpoints of the grid.\n",
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" \"\"\"\n",
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" \n",
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" if in1_len is not None or in2_len is not None:\n",
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" if in2_len is None:\n",
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" in2_len = in1_len\n",
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" elif in1_len is None:\n",
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" in1_len = in2_len\n",
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"\n",
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" lags = signal.correlation_lags(in1_len, in2_len, mode=mode)\n",
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"\n",
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" max_lag = max(lags)\n",
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" min_lag = min(lags)\n",
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" else:\n",
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" max_lag = np.inf\n",
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" min_lag = -np.inf\n",
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"\n",
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" if end is None:\n",
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" end = max_lag\n",
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" elif end > max_lag:\n",
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" raise ValueError(\"Grid end is too high\")\n",
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"\n",
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" if start is None:\n",
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" start = min_lag\n",
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" elif start < min_lag:\n",
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" raise ValueError(\"Grid start is too low\")\n",
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" \n",
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" if grid_size is None:\n",
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" grid_size = end - start\n",
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"\n",
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" return np.linspace(start, end, grid_size, dtype=int, endpoint=False)"
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"from lib.beacon import *"
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]
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},
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{
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@ -230,27 +32,6 @@
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"def beacon_time_delay(samplerate, ref_beacon, beacon):\n",
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" grid = correlation_grid(in1_len=len(ref_beacon), in2_len=len(beacon), mode='full')\n",
|
||||
" time_lag, errs = lag_gridsearch(grid, samplerate, ref_beacon, beacon)\n",
|
||||
"\n",
|
||||
" return time_lag, errs\n",
|
||||
"\n",
|
||||
"def beacon_phase_delay(samplerate, f_beacon, ref_beacon, beacon):\n",
|
||||
" time_delay, errs = beacon_time_delay(samplerate, ref_beacon, beacon)\n",
|
||||
"\n",
|
||||
" phase = time2phase(time_delay, f_beacon)\n",
|
||||
" phase_err = time2phase(errs, f_beacon)\n",
|
||||
" \n",
|
||||
" return phase, phase_err"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 4,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"us = 1e3 # ns\n",
|
||||
"ns = 1/us # us\n",
|
||||
|
|
@ -284,7 +65,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 5,
|
||||
"execution_count": 4,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
|
|
@ -378,7 +159,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 6,
|
||||
"execution_count": 5,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
|
|
|
|||
Loading…
Reference in New Issue