#deviation #stability #time #frequency #allan


Package to compute statistics to study systems stability

6 releases

0.1.2 Jan 5, 2022
0.1.1 Dec 27, 2021
0.0.3 Dec 26, 2021

#56 in Math

Download history 68/week @ 2021-12-21 14/week @ 2021-12-28 21/week @ 2022-01-04 10/week @ 2022-01-11

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Rust crates.io

crates.io crates.io License

Allantools (python lib) portage to Rust

This library allows easy computations of Allan deviation & similar statistics.
These statistical methods are mostly used in system stability studies.

Variances / Deviations

Compute Allan deviation over raw data:

  use allantools::*;
  let taus = tau::generator(tau::TauAxis::Octave, 2, 128); // [2, 4, 8, ... 128]
  let sampling_period = 1.0_f64; // [s]
  let (dev, errs) = deviation(&data, &taus, Deviation::Allan, sampling_period, false, false).unwrap();
alt text

This lib against stable32 on a well known signal.

Error bars

Only basic (biased) error bars following the 1/√N decay are currently produced


Improve statiscal confidence by using overlapped formulae

  let data: Vec<f64> = some_data();
  let taus = tau::generator(tau::TauAxis::Octave, 128);
  let overlapping = true;
  let sampling_period = 1.0_f64; // [s]
  let (var, errs) = deviation(&data, &taus, Deviation::Allan, sampling_period, false, overlapping).unwrap();

Fractionnal data

is fractional can be used to compute statistics over fractional (n.a) data:

  let data: Vec<f64> = some_data();
  let taus = tau::generator(tau::TauAxis::Octave, 10000);
  let is_fractional = true;
  let sampling_period = 1.0_f64; // [s]
  let ( adev, errs) = deviation(&data, &taus, Deviation::Allan, sampling_period, is_fractional, false).unwrap();
  let (oadev, errs) = deviation(&data, &taus, Deviation::Allan, sampling_period, is_fractional, true).unwrap();

Tau axis generator

The user can pass any τ serie to all computation methods.

This lib integrates a τ axis generator too, which is a convenient method to quickly pass a standard axis to a computation method. Several axis are known:

  • TauAxis::Octave is the most efficient
  • TauAxis::Decade is the standard and is efficient
  • TauAxis::All requires more computation
  let taus = tau::generator(tau::TauAxis::Decade, 1.0, 10000.0); // [1.0, 10.0, 100.0, ..., 10000.0]
alt text

Using TauAxis::All requires more computation but gives a total time granularity

  let taus = tau::generator(tau::TauAxis::All, 1.0, 100.0); // [1.0, 2.0, 3.0, ..., 99.0, 100.0]
alt text

Tau offset and error management

This library computes the requested statistics for all τ values, as long as $#964;(n) can be evaluated.
If τ (n) cannot be evaluated, computation stops and returns all previously evaluated offsets.

If not a single τ value is feasible, the lib returns Error::NotEnoughSamplesError

The user must pass a valid τ serie, otherwise:

  • TauAxis::NullTauValue: is returned when τ = 0 (non sense) is requested
  • TauAxis::NegativeTauValue: is return when τ < 0 (non physical) is requested
  • TauAxis::InvalidTauShape: shape is not an increasing (not necessarily steady) shape

Data & Noise generators

Some data generators were integrated or develpped for testing purposes:

  • White noise generator
  let x = allantools::noise::white_noise(
    -140.0_f64, // dBc/Hz
    1.0_f64, // (Hz)
    10000); // 10k samples
alt text
  • Pink noise generator
  let x = allantools::noise::pink_noise(
    -140.0_f64, // dBc @ 1Hz
    1.0_f64, // (Hz)
    1024); // 1k samples
alt text
Noise White PM Flicker PM White FM Flicker FM
adev -1 -1 -1/2 0
mdev -3/2 -1 -1/2 0
method utils::diff(noise::white) utils::diff(noise::pink) noise::white noise::pink

Power Law Identification

NIST LAG1D autocorrelation

NIST Power Law identification method[[46]]

This macro works well on data serie where one noise process is very dominant.

  let r = allantools::nist_lag1d_autocorr(&some_data);

Bias1 + R(n) identification method


Three Cornered Hat

Three cornered hat fashion statistics, to estimate a/b/c from a against b, b against c and c against a measurements.

   let a_against_b = some_measurements("a", "b");
   let b_against_c = some_measurements("b", "c");
   let c_against_a = some_measurements("c", "a");
   let taus = tau::tau_generator(tau::TauAxis::Octave, 10000.0);
   let sampling_period = 1.0;
   let is_fractionnal = false;
   let overlapping = true;

   let ((dev_a, err_a),(dev_b,err_b),(dev_c,err_c)) =
      three_cornered_hat(&a_against_b, &b_against_c, &c_against_a,
         &taus, sampling_period, is_fractionnal, overlapping, Deviation::Allan).unwrap();
alt text

Tools & utilities

cumsum : (python::numpy like) returns cummulative sum of a serie

   let data: Vec<f64> = some_data();
   allantools::utilities::cumsum(data, None);
   allantools::utilities::cumsum(data, Some(10E6_f64)); // opt. normalization

diff : (python::numpy like) returns 1st order derivative of a serie

   let data: Vec<f64> = some_data();
   allantools::utilities::diff(data, None);
   allantools::utilities::diff(data, Some(10E6_f64)); // opt. normalization

random : generates a pseudo random sequence 0 < x <= 1.0

   let data = allantools::utilities::random(1024); // 1k symbols 
   println!("{:#?}", data);

normalize : normalizes a sequence to 1/norm :

   let data: Vec<f64> = somedata(); 
   let normalized = allantools::utilities::normalize(
       2.0_f64 * std::f64::consts::PI); // 1/(2pi)

to_fractional_frequency : converts a raw data serie to fractional data.

   let data: Vec<f64> = somedata(); // sampled @ 10kHz
   let fract = allantools::utilities::to_fractional_frequency(data, 10E3); // :)

fractional_integral : converts a serie of fractional measurements to integrated measurements (like fractional frequency (n.a) to phase time (s)).

   let data: Vec<f64> = somedata(); // (n.a) 
   let fract = allantools::utilities::fractional_integral(data, 1.0); // sampled @ 1Hz :)

fractional_freq_to_phase_time : macro wrapper of previous function

phase_to_radians : converts phase time (s) to phase radians (rad)

   let data: Vec<f64> = somedata(); // (s)
   let data_rad = allantools::utilities::phase_to_radians(data);


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