Hadamard deviation

Formula

Hadamard variance

\[H\sigma_y^2(\tau)=\frac{1}{6\tau^2(N-3m)}\sum_{j=1}^{N-3m}\left(x_{j+3}-3x_{j+2}+3x_{j+1}-x_{j}\right)^2\]

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 if data 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 type AllTaus, 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)