Power Spectrum of Stochastic Pulse Sequences with Correlation between the Pulse Parameters

Abstract

The power spectrum $S\left(f\right)\mathrm{}$ of pulse sequences, which belong to the class of Markov processes, is calculated for the general case of a combined distribution $\gamma (\vartheta ,\tau ,h)$ that permits coupling between the pulse parameters: amplitude $h$, duration $\tau$, and time period $\vartheta$ preceding or following a pulse. Two special cases of coupling are considered in detail with respect to fluxtransport noise in superconductors: (i) With $\tau h=\mathrm{const}$, i.e., all pulses have the same time integral, $S\left(f\right)\mathrm{}$ exhibits at high frequencies an asymptotic $f^{-m}$ dependence regardless of the particular pulse shape, if the series expansion for the distribution of $\tau$ at small $\tau$ values starts with a term $\propto {\tau }^{m-1\mathrm{}}$. (ii) A relaxation time $\vartheta$ proportional to the pulse size $\tau h$, and an exponential distribution for $\vartheta$ leads to an asymptotic $f^2$ behavior at low frequencies, again practically independent of the pulse shape.