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Electrical Engineering

A periodic function f(x) is defined as 2, -1

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Concept explainers

Fourier Series

Most of the incidents studied in the field of Engineering and Science as a function of time. For example, current and voltage are in the alternating current circuit. These occasional activities can be analyzed in the activity components (fundamental frequency and harmonics) through a process called Fourier analysis.

Question

A periodic function f(x) is defined as
2, -1<x<0,
f (x)=-
[3x,
0<x<1.
f (x+2) = f (x)
Based on the above function,
a) Determine the period, p. Then, Sketch the graph of f(x) in range of –3 < x <3.
b) Determine whether the function f(x) is even, odd or neither even nor odd function and
state your reason.
c) Calculate the Fourier series of the function f(x).
d) By considering the summation up until n= 2, what is the Fourier series expansion
for f(x).

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