Representation and Analysis of Signals. Part XXVIII. Zero-Crossings of Shot-Noise Processes

摘要

The work is directed at the problem of computing beta, the expected number of zero-crossings per unit time, for random processes of shot-noise type. For the case that the underlying impulse response of the process has finite time duration, sufficient conditions for beta to be given in terms of an expression involving a characteristic function of the process are found. A series expansion for beta in powers of lambda, the parameter of the imbedded Poisson process, is developed, and beta(lambda) is shown to be an entire function. (Author)