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By adaptively approximating the characteristic function to the required power by cubic spline functions, the probability density function of a sum of pulse functions with random amplitude and delay, can be approximated with good accuracy and over a wide range. The efficacy of the approach is shown by the determination of the probability density function evolution of a pulse train. Simulation results...
A simple as possible random process - a random telegraph signal with independent amplitudes, and underpinned by a point process with inter-arrival times specified by a one sided Cauchy probability density function, is shown to have a 1/f power spectral density. Integral, and statistical, expressions for the number of points in a set interval, and the arrival time of the kth point, are specified. An...
Time domain definitions for finite bandwidth white noise, and filtered white noise, are detailed and are of pedagogical value. The associated power spectral density and autocorrelation functions are given. The potential Gaussianity of white noise is noted.
A model which facilitates the simulation of switching in a CMOS inverter, and a model for the associated PDF evolution, are proposed. The latter model is based on a Gaussian basis set. Simulation results, for the additive Gaussian white noise case, show, first, that the Gaussian assumption for the probability density function of the output jitter is valid at high input noise levels but with deviations...
Theory and results demonstrate, statistically and by implication, structurally, that the zero crossings of a generalized shot noise process are equivalent to those of a modified random telegraph signal based on grouping of Poisson points. The zero crossings are not statistically consistent with a Poisson point process.
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