Total deviation
Formula
total variance
\[Tot\,\sigma_y^2(\tau)=\frac{1}{2\tau^2(N-2)}\sum_{j=2}^{N-1}\left(x_{j-m}^*-2x_{j}^*+x_{j+m}^*\right)^2\]
Doc String
AllanDeviations.totaldev
— Method.totaldev(data, rate; [frequency=false], [overlapping=true], [taus=Octave]) Calculates the total 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.
Possible issues
totaldev
can be called with a non-overlapping calculation. This throws a warning because it is unusual to use but nevertheless faster.