Examination of time series through randomly broken windows

Abstract

In order to determine the Fourier transform of a quasi-periodic time series (linear problem), or the power spectrum of a stationary random time series (quadratic problem), data should be recorded without interruption over a long time interval. The effect of regular interruption such as the day/night cycle is well known. The effect of irregular interruption of data collection (the "breaking" of the window function) with the simplifying assumption that there is a uniform probability p that each interval of length tau, of the total interval of length T = N sub tau, yields no data, is investigated. For the linear case it is found that the noise-to-signal ratio will have a (one-sigma) value less than epsilon if N exceeds p(-1)(1-p)epsilon(-2). For the quadratic case, the same requirement is met by the less restrictive requirement that N exceed p(-1)(1-p)epsilon(-1)