Chapter 5 - Analysis of continuous and discrete time signals

Abstract

To understand the spectral representations between continuous time histories and their discrete time (sampled) counterparts, Chapter 5 first reviews the various frequency-domain transforms and their relationships. The chapter covers the Fourier and Laplace transforms, and the Fourier series that represent continuous time histories in the frequency domain. These concepts extend the introductory material in Volume I, Chapter 3, and allow for a rigorous discussion of sampling and aliasing. Chapter 5 then addresses discrete time records, and introduces frequency-domain transforms that are the discrete counterparts of the continuous transforms. The continuous and discrete transforms are the basic tools for designing time-domain filters that modify a time history’s spectral content. Procedures for designing finite impulse response (FIR) and infinite impulse response (IIR) filters are then introduced. The final section covers the Hilbert transform, which is useful for estimating time-varying amplitude and phase. The chapter concludes with references and solved problems that reinforce the material discussed in the chapter.