Dead-Time Modifications to Fast Fourier Transform Power Spectra

Abstract

Time series analysis in X-ray astronomy is complicated by the effects of detector dead time which can cause significant departures of power spectra from those expected from simple Poisson statistics. In this paper we study the effects of both the paralyzable and nonparalyzable dead times on the underlying time series which obeys Poisson counting statistics. We present analytical formulae for the autocorrelation function, auto-covariances, and power spectra, for both kinds of dead time. These formulae, taken as a whole, offer a general qualitative and quantitative framework to further understand the effects of dead time in an X-ray detection and data processing system.