Fourier Transforms, Filtering, Probability and Random Processes

This book provides backgrounds and the mathematical methods necessary to understand the basic transforms in signal processing and linear systems to prepare for in depth study of analog and digital communications systems. This tutorial presentation provides developments of Fourier series and other orthogonal series, including trigonometric and complex exponential Fourier series, least squares approximations and generalized Fourier series, and the spectral content of periodic signals. This text thoroughly covers Fourier transform pairs for continuous time signals, Fourier transform properties, and the magnitude and phase of Fourier transforms. The author includes discussions of techniques for the analysis of continuous time linear systems in the time and frequency domains with particular emphasis on the system transfer function, impulse response, system/filter bandwidth, power and energy calculations,and the time domain sampling theorem.