The analysis of finite-length records of fluctuating signals

The problem discussed is that of estimating the characteristics of a signal from a record of finite length by Fourier-type analysis or by direct measurement. The paper is an attempt to present the fundamentals of the problem in a coherent form and with the simplest possible mathematics: the results given are not new. The main discussion is of the accuracy of estimates of the power spectra and r.m.s. amplitudes of stationary random Gaussian processes: these have the characteristics of filtered random noise and include a class of signals of great practical importance. The arguments also apply to the problem of estimating the maximum speed with which a signal can be measured and analysed directly.