Random phenomena have their basis in the nature of the physical order (., the nature of electron movement) and limit the performance of many systems including electronic and communication systems. For example, the minimum sensitivity of an amplifier and the distance a signal can be transmitted and recovered, are both limited by random signal variations. On the other hand, there are applications where introduced randomness will enhance aspects of system performance. | Principles of Random Signal Analysis and Low Noise Design The Power Spectral Density and Its Applications. Roy M. Howard Copyright 2002 John Wiley Sons Inc. ISBN 0-471-22617-3 1 Introduction Random phenomena have their basis in the nature of the physical order . the nature of electron movement and limit the performance of many systems including electronic and communication systems. For example the minimum sensitivity of an amplifier and the distance a signal can be transmitted and recovered are both limited by random signal variations. On the other hand there are applications where introduced randomness will enhance aspects of system performance. One example is where a low level randomly varying waveform is added to a repetitive signal to improve the resolution in signal values obtained by an analogue to digital converter and after averaging Potzick 1999 Gray 1993 . Further in recent years there has been increasing interest in stochastic resonance which occurs when the system response to a weak periodic signal is enhanced by an increase in the level of random variations associated with the system Luchinsky 1999 Hanggi 2000 . The importance of random phenomena has led to an increasing number of theoretical results as can be found in books such as Gardner 1990 Papoulis 2002 and Taylor 1998 . In communications and electronics a standard way of characterizing random phenomenon is through a power spectral density which for example facilitates derivation of the signal to noise ratio of a system operating under prescribed conditions. There are two standard approaches for defining the power spectral density. First there is a direct Fourier approach. Second and more commonly an approach based on the Fourier transform of an autocorrelation function. With the direct Fourier approach the power spectral density of a single signal x for the interval 0 T is defined as G T f X Ttf 2 where X is the Fourier transform of x evaluated over the interval 0 T . The alternative .
