Allan deviation and related time/frequency statistics

## Project description

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

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