Skip to content
CloverTexts Logo 🍀 CloverTexts Library

The Fourier Series

← Back to Fundamentals of Electric Circuits Overview

The Fourier Series

Research is to see what everybody else has seen, and think what nobody has thought.

—Albert Szent Györgyi

Enhancing Your Skills and Your Career

ABET EC 2000 criteria (3.j), “a knowledge of contemporary issues.”

Engineers must have knowledge of contemporary issues. To have a truly meaningful career in the twenty-first century, you must have knowledge of contemporary issues, especially those that may directly af fect your job and/or work. One of the easiest ways to achieve this is to read a lot newspapers, magazines, and contemporary books. As a student enrolled in an ABET-accredited program, some of the courses you take will be directed toward meeting this criteria.

ABET EC 2000 criteria (3.k), “an ability to use the techniques, skills, and modern engineering tools necessary for engineering practice.”

The successful engineer must ha ve the “ability to use the techniques, skills, and modern engineering tools necessary for engineering practice.” Clearly, a major focus of this te xtbook is to do just that. Learning to use skillfully the tools that facilitate your working in a modern “knowledge capturing integrated design environment” (KCIDE) is fundamental to your performance as an engineer . The ability to w ork in a modern KCIDE environment requires a thorough understanding of the tools associated with that environment.

The successful engineer , therefore, must k eep abreast of the ne w design, analysis, and simulation tools. That engineer must also use those tools until he or she is comfortable with using them. The engineer also must make sure software results are consistent with real-world actualities. It is probably in this area that most engineers have the greatest difficulty. Thus, successful use of these tools requires constant learning and relearning the fundamentals of the area in which the engineer is working.

Photo by Charles Alexander

Historical

Jean Baptiste Joseph Fourier (1768–1830), a French mathematician, first presented the series and transform that bear his name. Fourier’s results were not en thusiastically received by the scientific world. He could not even get his work published as a paper.

Born in Auxerre, France, Fourier was orphaned at age 8. He attended a local military college run by Benedictine monks, where hedemonstrated great proficiency in mathematics. Like most of his contemporaries, Fourier was swept into the politics of the French Revolution. He played an important role in Napoleon’s expeditions to Egypt in the later 1790s. Due to his political involvement, he narrowly escaped death twice.

Learning Objectives

By using the information and exercises in this chapter you will be able to:

    1. Understand the trigonometric Fourier series and know how to determine the Fourier series with a variety of periodic functions.
    1. Effectively use the Fourier series to analyze the response of circuits to a variety of periodic sources.
    1. Know how the symmetrical characteristics of some wave shapes can make determining the Fourier series of classes of periodic functions easier to determine.
    1. Understand how to determine average power and rms values associated with periodic functions.
    1. Understand the use of the discrete Fourier transform and the fast Fourier transform.