Welcome to rhos documentation!
rhos (recursive high order statistics) is a python module to compute recursive mean, variance and high-order statistics on 1D signals.
Each function is implemented in pure python (functions ending in _py,
useful for algorithm reference), as well as using a faster approach based
on scipy.signal.lfilter().
Functions
Recursive high-order statistics for Python.
- copyright
2022 Claudio Satriano <satriano@ipgp.fr>
- license
GNU Lesser General Public License, Version 3 (https://www.gnu.org/copyleft/lesser.html)
- rhos.rec_mean_py(signal, C)[source]
Recursive mean of a signal.
μ[i] = C·signal[i] + (1-C)·μ[i-1]
- Parameters
- Returns
the recursive mean, with the same length than signal
- Return type
- Raises
ValueError – if C is not in the [0, 1] interval
Warning
This is a pure python reference implementation. Use
recursive_mean()for a faster implementation.
- rhos.rec_mean(signal, C)[source]
Recursive mean of a signal.
μ[i] = C·signal[i] + (1-C)·μ[i-1]
- Parameters
- Returns
the recursive mean, with the same length than signal
- Return type
- Raises
ValueError – if C is not in the [0, 1] interval
Note
Fast implementation, using
scipy.signal.lfilter().
- rhos.rec_variance_py(signal, C, definition=0)[source]
Recursive variance of a signal.
Defined as in Poiata et al. [2016] (definition 0):
σ²[i] = C·(signal[i]-μ[i-1])² + (1-C)·σ²[i-1]
Or, defined as in Langet et al. [2014] (definition 1):
σ²[i] = C·(signal[i]-μ[i])² + (1-C)·σ²[i-1]
For both definitions:
μ[i] = C·signal[i] + (1-C)·μ[i-1]
- Parameters
- Returns
the recursive variance, with the same length than signal
- Return type
- Raises
ValueError – if C is not in the [0, 1] interval
ValueError – if definition is not 0 or 1
Warning
This is a pure python reference implementation. Use
recursive_variance()for a faster implementation.
- rhos.rec_variance(signal, C, definition=0)[source]
Recursive variance of a signal.
Defined as in Poiata et al. [2016] (definition 0):
σ²[i] = C·(signal[i]-μ[i-1])² + (1-C)·σ²[i-1]
Or, defined as in Langet et al. [2014] (definition 1):
σ²[i] = C·(signal[i]-μ[i])² + (1-C)·σ²[i-1]
For both definitions:
μ[i] = C·signal[i] + (1-C)·μ[i-1]
- Parameters
- Returns
the recursive variance, with the same length than signal
- Return type
- Raises
ValueError – if C is not in the [0, 1] interval
ValueError – if definition is not 0 or 1
Note
Fast implementation, using
scipy.signal.lfilter().
- rhos.rec_hos_py(signal, C, order=4, var_min=- 1, definition=0)[source]
Recursive high order statistics (hos) of a signal.
Defined as in BackTrackBB (definition 0):
hos[i] = C·(signal[i]-μ[i-1])ⁿ / (σ²[i])ⁿᐟ² + (1-C)·hos[i-1]
with
σ²[i] = C·(signal[i]-μ[i-1])² + (1-C)·σ²[i-1]
Note
This is the actual implementation in the BackTrackBB source code, which does not correspond to equation 7 of Poiata et al. [2016] or equation 1 of Poiata et al. [2018].
Or, defined as in Langet et al. [2014] (definition 1):
hos[i] = C·(signal[i]-μ[i])ⁿ / (σ²[i])ⁿᐟ² + (1-C)·hos[i-1]
with
σ²[i] = C·(signal[i]-μ[i])² + (1-C)·σ²[i-1]
For both definitions:
μ[i] = C·signal[i] + (1-C)·μ[i-1]
- Parameters
- Returns
the recursive hos, with the same length than signal
- Return type
- Raises
ValueError – if C is not in the [0, 1] interval
ValueError – if definition is not 0 or 1
Warning
This is a pure python reference implementation. Use
recursive_hos()for a faster implementation.
- rhos.rec_hos(signal, C, order=4, var_min=- 1, definition=0)[source]
Recursive high order statistics (hos) of a signal.
Defined as in BackTrackBB (definition 0):
hos[i] = C·(signal[i]-μ[i-1])ⁿ / (σ²[i])ⁿᐟ² + (1-C)·hos[i-1]
with
σ²[i] = C·(signal[i]-μ[i-1])² + (1-C)·σ²[i-1]
Note
This is the actual implementation in the BackTrackBB source code, which does not correspond to equation 7 of Poiata et al. [2016] or equation 1 of Poiata et al. [2018].
Or, defined as in Langet et al. [2014] (definition 1):
hos[i] = C·(signal[i]-μ[i])ⁿ / (σ²[i])ⁿᐟ² + (1-C)·hos[i-1]
with
σ²[i] = C·(signal[i]-μ[i])² + (1-C)·σ²[i-1]
For both definitions:
μ[i] = C·signal[i] + (1-C)·μ[i-1]
- Parameters
- Returns
the recursive hos, with the same length than signal
- Return type
- Raises
ValueError – if C is not in the [0, 1] interval
ValueError – if definition is not 0 or 1
Note
Fast implementation, using
scipy.signal.lfilter().
References
- 1(1,2,3,4)
N. Poiata, C. Satriano, J.-P. Vilotte, P. Bernard, and K. Obara. Multiband array detection and location of seismic sources recorded by dense seismic networks. Geophysical Journal International, 205(3):1548–1573, 2016. doi:10.1093/gji/ggw071.
- 2(1,2,3,4)
N. Langet, A. Maggi, A. Michelini, and F. Brenguier. Continuous kurtosis-based migration for seismic event detection and location, with application to piton de la fournaise volcano, la reunion. Bulletin of the Seismological Society of America, 104(1):229–246, 2014. doi:10.1785/0120130107.
- 3(1,2)
N. Poiata, J.-P. Vilotte, P. Bernard, C. Satriano, and K. Obara. Imaging different components of a tectonic tremor sequence in southwestern japan using an automatic statistical detection and location method. Geophysical Journal International, 213(3):2193–2213, 2018. doi:10.1093/gji/ggy070.