A python library for calculating Allan deviation and related time & frequency statistics. LGPL v3+ license.
- Development at https://github.com/aewallin/allantools
- Installation package at https://pypi.python.org/pypi/AllanTools
- Discussion group at https://groups.google.com/d/forum/allantools
- Documentation available at https://allantools.readthedocs.org
Input data should be evenly spaced observations of either fractional frequency, or phase in seconds. Deviations are calculated for given tau values in seconds.
| Function | Description | Comment |
|---|---|---|
adev() |
Allan deviation | Classic - use only if required - relatively poor confidence. |
oadev() |
Overlapping Allan deviation | General purpose - most widely used - first choice |
mdev() |
Modified Allan deviation | Used to distinguish between White and Flicker Phase Modulation. |
tdev() |
Time deviation | Based on modified Allan variance. |
hdev() |
Hadamard deviation | Rejects frequency drift, and handles divergent noise. |
ohdev() |
Overlapping Hadamard deviation | Better confidence than normal Hadamard. |
pdev() |
Parabolic deviation | Estimate uncertainty of Omega-counter data |
totdev() |
Total deviation | Better confidence at long averages for Allan deviation. |
mtotdev() |
Modified total deviation | Modified Total deviation. Better confidence at long averages for modified Allan |
ttotdev() |
Time total deviation | |
htotdev() |
Hadamard total deviation | |
theo1() |
Theo1 deviation | Theo1 is a two-sample variance with improved confidence and extended averaging factor range. |
mtie() |
Maximum Time Interval Error | |
tierms() |
Time Interval Error RMS | |
gradev() |
Gap resistant overlapping Allan deviation | |
gcodev() |
Groslambert Covariance | Improved three-corner-hat analysis |
Noise generators for creating synthetic datasets are also included:
- violet noise with f^2 PSD
- white noise with f^0 PSD
- pink noise with f^-1 PSD
- Brownian or random walk noise with f^-2 PSD
More details on available statistics and noise generators : full list of available functions
see /tests for tests that compare allantools output to other (e.g. Stable32) programs. More test data, benchmarks, ipython notebooks, and comparisons to known-good algorithms are welcome!
Install from pypi:
pip install allantools
Latest version + examples, tests, test data, iPython notebooks : clone from github, then install
python setup.py install
(see python setup.py --help install for install options)
These commands should be run as root for system-wide installation, or you can use the --user option to install for your account only. Exact command names may vary depending on your OS / package manager / target python version.
We can call allantools with only one parameter - an array of phase data. This is suitable for time-interval measurements at 1 Hz, for example from a time-interval-counter measuring the 1PPS output of two clocks.
>>> import allantools >>> x = allantools.noise.white(10000) # Generate some phase data, in seconds. >>> (taus, adevs, errors, ns) = allantools.oadev(x)
when only one input parameter is given, phase data in seconds is assumed when no rate parameter is given, rate=1.0 is the default when no taus parameter is given, taus='octave' is the default
Note that allantools assumes non-dimensional frequency data input. Normalization, by e.g. dividing all data points with the average frequency, is left to the user.
>>> import allantools >>> import pylab as plt >>> import numpy as np >>> t = np.logspace(0, 3, 50) # tau values from 1 to 1000 >>> y = allantools.noise.white(10000) # Generate some frequency data >>> r = 12.3 # sample rate in Hz of the input data >>> (t2, ad, ade, adn) = allantools.oadev(y, rate=r, data_type="freq", taus=t) # Compute the overlapping ADEV >>> fig = plt.loglog(t2, ad) # Plot the results >>> # plt.show()
New in 2016.11 : simple top-level API, using dedicated classes for data handling and plotting.
import allantools # https://github.com/aewallin/allantools/
import numpy as np
# Compute a deviation using the Dataset class
a = allantools.Dataset(data=np.random.rand(1000))
a.compute("mdev")
# New in 2019.7 : write results to file
a.write_results("output.dat")
# Plot it using the Plot class
b = allantools.Plot()
# New in 2019.7 : additional keyword arguments are passed to
# matplotlib.pyplot.plot()
b.plot(a, errorbars=True, grid=True)
# You can override defaults before "show" if needed
b.ax.set_xlabel("Tau (s)")
b.show()
Jupyter notebooks are interactive python scripts, embedded in a browser, allowing you to manipulate data and display plots like easily. For guidance on installing jupyter, please refer to https://jupyter.org/install.
See /examples for some examples in notebook format.
github formats the notebooks into nice web-pages, for example
- https://github.com/aewallin/allantools/blob/master/examples/noise-color-demo.ipynb
- https://github.com/aewallin/allantools/blob/master/examples/three-cornered-hat-demo.ipynb
- Anders E.E. Wallin, anders.e.e.wallin "at" gmail.com , https://github.com/aewallin
- Danny Price, https://github.com/telegraphic
- Cantwell G. Carson, carsonc "at" gmail.com
- Frédéric Meynadier, https://github.com/fmeynadier
- Yan Xie, https://github.com/yxie-git
- Erik Benkler, https://github.com/EBenkler