Frequency Domain Analysis of Signals and Systems

Telecommunication signals and systems can be characterised in both the time and the frequency domains. This chapter begins with a discussion on the Fourier series applicable to continuous-time periodic signals. Using a mix of heuristic, graphical, and mathematical approaches, it explores the topic of Fourier series at a depth and breadth that are considered complete for the needs of modern engineering. The chapter emphasises how to derive the Fourier series either from first principles by evaluating integrals or by applying some of its properties. It then employs the tool of Fourier series to analyse flat-top sampling, sinusoidal pulse trains, and binary amplitude shift keying with very interesting and insightful results. The Fourier series may also be adapted to obtain a discrete Fourier transform, which is applicable to discrete-time signals. The chapter briefly introduces the Laplace transform and z-transform.