x(t) for k E N are given as follows (rest of the Fourier coefficients are zero fo kEN). 3 Co = 1, C₁ = ², C3 = 2j Write the signal x(t) in time domain and in simplified form (without any complex exponentials).

x(t) for k E N are given as follows (rest of the Fourier coefficients are zero fo kEN). 3 Co = 1, C₁ = ², C3 = 2j Write the signal x(t) in time domain and in simplified form (without any complex exponentials).

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

fundamental period is given as To= . The non-zero Fourier coefficients of
x(t) for k E N are given as follows (rest of the Fourier coefficients are zero for
KEN).
3
Co = 1,
= 1, C₁
C3 = 2j
"
2
Write the signal x(t) in time domain and in simplified form (without any
complex exponentials).

Fourier coefficients of the following signal. Also, write the signal in terms of
complex exponentials (i.e. using Fourier series).
x(t) = −2+ 4 cos(3t) cos(t – π/2) + 3 ej4t
[Hint: 2 cos(A) cos(B) = cos(A+B) + cos (A − B)]

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