I need help with part d and part e. Please show clearly how to solve those parts. Thank you. Fourier Series- Exponential FormConsider the periodic signal x(t) depicted in Figure 1.x(t)1-5-33 4 5tFigure 1: Periodic signalWe wish to obtain the signal harmonics via the Fourier Series.a) Take the signal from the time domain to the 0 domain.b) Find an expression for the Fourier coefficients c,Use this expression to find Co,c,c2,C3,C4,Cg in polar formc) Plot |c, and &c, as a function of n for n=0,1,2,3,4,5d) From these plots, obtain the first harmonics (amplitude and phase) forn = 0,1,2,3,4,5 . Write a Fourier series expansion in the form x(0) =E4, cos(n® + 9,)e) Take the signal back to the time domain. Write a Fourier series expansion inthe form x(1) =£4¸cos(n@,t+ P,)0

We are given the following periodic signal x(t): (d) we have to plot Cn and ∠Cn as a function of n…

d) From these plots, obtain the first harmonics (amplitude and phase) for n = 0,1, 2,3, 4,5. Write a Fourier series expansion in the formx(0) = 4, cos(n@ +9,) e) Take the signal back to the time domain. Write a Fourier series expansion in the form x(1) = £4, cos(no,t+9,)

d) From these plots, obtain the first harmonics (amplitude and phase) for n = 0,1, 2,3, 4,5. Write a Fourier series expansion in the formx(0) = 4, cos(n@ +9,) e) Take the signal back to the time domain. Write a Fourier series expansion in the form x(1) = £4, cos(no,t+9,)

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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Question

I need help with part d and part e. Please show clearly how to solve those parts. Thank you.

Fourier Series- Exponential Form
Consider the periodic signal x(t) depicted in Figure 1.
x(t)
1
-5
-3
3 4 5
t
Figure 1: Periodic signal
We wish to obtain the signal harmonics via the Fourier Series.
a) Take the signal from the time domain to the 0 domain.
b) Find an expression for the Fourier coefficients c,
Use this expression to find Co,c,c2,C3,C4,Cg in polar form
c) Plot |c, and &c, as a function of n for n=0,1,2,3,4,5
d) From these plots, obtain the first harmonics (amplitude and phase) for
n = 0,1,2,3,4,5 . Write a Fourier series expansion in the form x(0) =
E4, cos(n® + 9,)
e) Take the signal back to the time domain. Write a Fourier series expansion in
the form x(1) =£4¸cos(n@,t+ P,)
0

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