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 |
✓ | ✓ | ✓ | ✓ |
| Build & Tests (Julia v1.0.0 & upwards) |
Code test coverage | Documentation | ||
|---|---|---|---|---|
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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.
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/consecutiveEvery 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 possibleThis 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