A Signal Theoretic Introduction to Random Processes

1A SIGNAL THEORETIC INTRODUCTION TO RANDOM PROCESSES

1.1 INTRODUCTION

Consistent with the nature of the physical universe, the technical world, and the social world and at the usual levels of observation, randomness is ubiquitous. Consistent with this, randomness has received significant attention over human history and prehistory. The appearance of gods, and associated offerings to such deities, in early civilizations was, in part, an attempt to understand the randomness inherent in nature and to have control over this variability. As our understanding of the nature of the physical universe has expanded, interest in random phenomena, and its characterization, has increased significantly. Today, the accumulated knowledge on characterizing randomness is vast. Cohen ( 2005 ) provides a good overview of part of the more recent scientific endeavor to understand and characterize random phenomena. Meyer ( 2009 ) provides a historical perspective on the mathematical development of stochastic process theory from the 1940s.

Random phenomena occur widely in the physical, social, and technical worlds, and well-known examples include the variation, with time, in measures of the weather (wind velocity, temperature, humidity, etc.), economic activity (inflation rate, stock indexes, currency exchange rates, etc.), an individual’s physical state (heart rate, blood pressure, feeling of well-being, etc.), and technical entities (the information flow to a mobile communication device, the fuel economy ...