ON THE STATISTICAL PROPERTIES OF TRANSIENT NOISE SIGNALS

Abstract

Abstract : A class of random transient signals has been defined as the product of a deterministic envelope waveform of finite integral square and a continuous random process with a well-defined power spectrum and autocorrelation function. The time average autocorrelation function and energy density spectrum of the resulting waveform have been found to be random variables at every value of their arguments. The means and variances of these random variables are derived as functions of the characteristics of the envelope and original noise process. The average autocorrelation function is found to be the product of the autocorrelation functions of envelope and noise, and the average spectrum is given by the convolution of the energy spectrum of the envelope function and the power spectrum of the noise. Examples of the mean and variance calculations are presented for both rectangular and decaying exponential pulse of both broad and narrow band noise. Finally, the implications of these findings for measurement programs and monopulse signal processing are discussed.