AllanTools

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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
`adev()`	Allan deviation
`oadev()`	Overlapping Allan deviation
`mdev()`	Modified Allan deviation
`tdev()`	Time deviation
`hdev()`	Hadamard deviation
`ohdev()`	Overlapping Hadamard deviation
`totdev()`	Total deviation
`mtotdev()`	Modified total deviation
`ttotdev()`	Time total deviation
`htotdev()`	Hadamard total deviation
`theo1()`	Theo1 deviation
`mtie()`	Maximum Time Interval Error
`tierms()`	Time Interval Error RMS
`gradev()`	Gap resistant overlapping Allan deviation

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!

Installation

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.

Basic usage

Minimal example, phase data

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

Frequency data example

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_result("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 with examples

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

Authors

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

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