# CHAPTER 15

*Fourier Series and Fourier Transform*

**IN THIS CHAPTER**

**15.1** Introduction

**15.2** The Fourier Series

**15.3** Symmetry of the Function *f*(*t*)

**15.4** Fourier Series of Selected Waveforms

**15.5** Exponential Form of the Fourier Series

**15.6** The Fourier Spectrum

**15.7** Circuits and Fourier Series

**15.8** Using PSpice to Determine the Fourier Series

**15.9** The Fourier Transform

**15.10** Fourier Transform Properties

**15.11** The Spectrum of Signals

**15.12** Convolution and Circuit Response

**15.13** The Fourier Transform and the Laplace Transform

**15.14** How Can We Check … ?

**15.15 DESIGN EXAMPLE**—DC Power Supply

**15.16** Summary

Problems

PSpice Problems

Design Problems

## 15.1 *Introduction*

This chapter introduces the Fourier series and the Fourier transform. The Fourier series represents a nonsinusoidal periodic waveform as a sum of sinusoidal waveforms. The Fourier series is useful to us in two ways:

- The Fourier series shows that a periodic waveform consists of sinusoidal components at different frequencies. That allows us to think about the way in which the waveform is distributed in frequency. For example, we can give meaning to such expressions as “the high-frequency part of a square wave.”
- We can use superposition to find the steady-state response of a circuit to an input represented by a Fourier series and, thus, determine the steady-state response of the circuit to the periodic waveform.

We obtain the Fourier ...