AllanTools
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 


Allan deviation 
Classic  use only if required  relatively poor confidence. 

Overlapping Allan deviation 
General purpose  most widely used  first choice 

Modified Allan deviation 
Used to distinguish between White and Flicker Phase Modulation. 

Time deviation 
Based on modified Allan variance. 

Hadamard deviation 
Rejects frequency drift, and handles divergent noise. 

Overlapping Hadamard deviation 
Better confidence than normal Hadamard. 

Parabolic deviation 
Estimate uncertainty of Omegacounter data 

Total deviation 
Better confidence at long averages for Allan deviation. 

Modified total deviation 
Modified Total deviation. Better confidence at long averages for modified Allan 

Time total deviation 


Hadamard total deviation 


Theo1 deviation 
Theo1 is a twosample variance with improved confidence and extended averaging factor range. 

Maximum Time Interval Error 


Time Interval Error RMS 


Gap resistant overlapping Allan deviation 


Groslambert Covariance 
Improved threecornerhat 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 knowngood 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 systemwide 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 timeinterval measurements at 1 Hz, for example from a timeintervalcounter 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 nondimensional 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 toplevel 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 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 webpages, for example