Max. time interval error

# Maximum time interval error

## Formula

Maximum time interval error

$Mtie(\tau)=\operatorname{max}_{1\leq k\leq N-n}\left(\operatorname{max}_{k\leq t\leq k+n}(x_t)-\operatorname{min}_{k\leq t\leq k+n}(x_t)\right)$

## Doc String

mtie(data, rate; [frequency=false], [overlapping=true], [taus=Octave]) Calculates the maximal time interval error

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)

• tau: Taus which where used.
• deviation: Deviations calculated.
• error: Respective errors.
• count: Number of contributing terms for each deviation.

## Possible issues

• mtie in itself needs a great amount of computations and can be very slow for big taus with many data points. When computations need too much time, consider reducing the number of taus and/or especially using smaller taus.
• Mtie can be called with a non-overlapping calculation. This throws a warning because it is unusual to use but nevertheless faster.