Spectral Analysis 1 – The Fourier Series in Modern Communications

This chapter explains how to analyze the frequency content of a periodic signal and shows how to reconstruct the signal if its frequency content is known, an operation called spectral synthesis. It introduces the basics of spectral analysis and spectral synthesis, distinguishes between time domain and frequency domain, and applies the Fourier series to find the spectrum of a periodic signal. The chapter describes how to find the Fourier series for various types of periodic signals and demonstrates the effect of filtering on signals from the standpoint of spectral analysis. It explains the concept of harmonic distortion and shows that the harmonic distortion is the phenomenon where an output signal contains more harmonics than an input signal. The chapter describes the mathematical foundation of the Fourier series and explains the power spectrum of periodic signals. It also introduces the concept of power‐bandwidth trade‐off in modern communications.