Chapter 5 - Real and Complex Fourier Series

Abstract

This chapter introduces the Fourier series in the real and complex form. The Fourier series provides a basis for analysis of signals in the frequency domain. First we develop the Fourier series as a technique to represent arbitrary periodic functions as a summation of sine and cosine waves. Subsequently, it is shown that the complex version of the Fourier series is simply an alternative notation. At the end of this chapter, the Fourier series technique is applied to decompose periodic functions into their cosine and sine components. Because the underlying principle is to represent waveforms as a summation of periodic cosine and sine waves with different frequencies, one can interpret the Fourier analysis as a technique for examining signals in the frequency domain.