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The NUSADC uses an additive "dither signal" to force threshold crossing events and achieve a predictable average sampling rate.
The boundary, or interface, ∂ B ( t ) is defined by the threshold crossing condition u ( x, t ) = h.
The TOA statistics are modeled and analyzed for a UWB receiver using threshold crossing detection of a pulse signal with noise.
One could also develop the linear stability analysis by considering perturbations of the threshold crossing points along the lines of Amari [20].
By making the Poisson assumption of independent upcrossings, extreme exceedance probabilities are predicted via the mean threshold crossing rate, using numerical solutions of the stationary Fokker Planck (FPK) equation.
Since we are using closed-form solutions for the orbits of our system, the only source of numerical error other than machine error arises due to the tolerance selected when computing the threshold crossing times for V.
We show that this leads to strong beyond-pairwise correlations that is, correlations that cannot be captured by maximum entropy models that extrapolate from pairwise statistics—as for earlier work with discrete threshold crossing (dichotomous Gaussian) models.
The threshold crossing procedure of the receiver for the noise-only case and the case when a pulse plus noise is received has been unified to a common first-crossing problem in a continuous random process.
The threshold for spike detection was set to −4.5 SD (standard deviations) and the spike waveforms were measured in a time window 1400 μs long and beginning 150 μs before threshold crossing.
Samples with a threshold crossing point >32 cycles for the genomic PCR were deemed poorly amplifiable and excluded from analysis.
More specifically this implies that the window period is the mean observable threshold crossing time, conditional on assay progression (i.e. actually reaching the threshold).
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