Hadamard deviation
Formula
Hadamard variance
\[H\sigma_y^2(\tau)=\frac{1}{6\tau^2(N-3m)}\sum_{j=1}^{N-3m}\left(x_{j+3}-3x_{j+2}+3x_{j+1}-x_{j}\right)^2\]
Doc String
AllanDeviations.hadamarddev
— Method.hadamarddev(data, rate; [frequency=false], [overlapping=true], [taus=Octave]) Calculates the hadamard deviation
#parameters:
<data>
: The data array to calculate the deviation from either as as phases or frequencies.<rate>
: The rate of the data given.[frequency]
: True ifdata
contains frequency data otherwise (default) phase data is assumed.[overlapping]
: True (default) to calculate overlapping deviation, false otherwise.[taus]
: Taus to calculate the deviation at. This can either be an AllanTauDescriptor typeAllTaus, Decadade, HalfDecade, Octave, HalfOctave, QuarterOctave
, an array of taus to calculate at, a float number to build a custom log-scale on or an integer to build a specific number of log spaced points.
#returns: named tupple (tau, deviation, error, count)
tau
: Taus which where used.deviation
: Deviations calculated.error
: Respective errors.count
: Number of contributing terms for each deviation.