AllanDeviations.jl is a package for the Julia programming language and provides various frequency- and phase-stability deviations (or variances) in overlapping and consecutive forms.

Currently implemented are:

Deviation	Function name	Phase Data	Frequency Data	Consecutive	Overlapping
Allan deviation	allandev	✓	✓	✓	✓
Modified Allan deviation	mallandev	✓	✓	✓	✓
Hadamard deviation	hadamarddev	✓	✓	✓	✓
Time deviation	timedev	✓	✓	✓	✓
Total deviation	totaldev	✓	✓	✓	✓
Maximal time interval error	mtie	✓	✓	✓	✓

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Build & Tests (Julia v1.0.0 & upwards)		Code test coverage		Documentation

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Usage

Installing (v1.0.0 and higher)

To install AllanDeviations.jl open up a Julia REPL/Console and type:

using Pkg;
Pkg.add("AllanDeviations")

This installs the package along with any dependencies needed.

Example code

The following code calculates the overlapping Allan deviation of a given data array arr and rate r with log2 spaced averaging times τ.

using AllanDeviations

(tau, deviation, error, count) = allandev(arr, r)			#assuming phase data

(tau, deviation, error, count) = allandev(arr, r, frequency = true)	#assuming frequency data
(tau, deviation, error, count) = allandev(arr, r, overlapping = false)	#non-overlapping/consecutive

Every function returns a simple named tuple (tau, deviation, error, count). tau is an array of the averaging times used. deviation are the respective calculated deviations, error the respective errors of the deviations and count is the number of terms contributing to every deviation.
The errors are calculated by error .= deviation ./ sqrt.(count).

The averaging times τ can also be finely tuned:

using AllanDeviations

allandev(arr, r)				#log_2 spaced tau distribution: octave

allandev(arr, r, taus = AllTaus)		#uses every possible tau value

allandev(arr, r, taus = Octave)			#log_2 spaced: octave (default)
allandev(arr, r, taus = HalfOctave)		#log_1.5 spaced: half octave
allandev(arr, r, taus = QuarterOctave)		#log_1.25 spaced: quarter octave
allandev(arr, r, taus = Decade)			#log_10 spaced: decade
allandev(arr, r, taus = HalfDecade)		#log_5 spaced: half decade

allandev(arr, r, taus = 1.1)			#log_1.1 spaced

allandev(arr, r, taus = [1.0, 2.0, 3.0])	#calculates at τ = 1.0, τ = 2.0 and τ = 3.0 if possible
allandev(arr, r, taus = [0.4])			#calculates at τ = 0.4 if possible

CSV example

This example shows how to load data from a csv file (via the CSV package), calculate the overlapping allan deviation with it and to output a plot (via the Plots package) in the same directory:

using AllanDeviations, CSV, Plots

data = CSV.read("fractionalFrequencyData.csv")	#load data
freq = data[:, 2]				#extract fractional frequency
rate = length(data[:, 1]) / data[end, 1]	#calculate rate

result = allandev(freq, rate, frequency = true)	#calculate overlapping allan deviation

plot(result.tau, result.deviation, xscale = :log10, yscale = :log10) #log-log plot everything
savefig("allanDevPlot.png") #save the plot

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References

• NIST - Riley, William J. "Handbook of frequency stability analysis." (2008): 81.
• C Reference implementations: leapsecond.com
• Python Package: AllanTools