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# 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 ...

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