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Fourier Series- Exponential Form Consider the periodic signal x(t) depicted in Figure 1.

Fourier Series- Exponential Form Consider the periodic signal x(t) depicted in Figure 1.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Please help solve the question shown in the photo. There is only 1 question but it contains a couple different parts. I want to understand fully how to solve the entire problem so please show all the steps to all parts. Thank you.

Fourier Series- Exponential Form Consider the periodic signal x(t) depicted in Figure 1. x(t) 1 -4 -5 -3 3 4 5 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 e domain. b) Find an expression for the Fourier coefficients c, Use this expression to find Co,C1,C2,C3,C4,C5 in polar form c) Plot c, and ác, 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) =4, cos(n0 + P,) n=0 e) Take the signal back to the time domain. Write a Fourier series expansion in the form x(1) = £4 cos(n@,t +P„) n=0
Transcribed Image Text:Fourier Series- Exponential Form Consider the periodic signal x(t) depicted in Figure 1. x(t) 1 -4 -5 -3 3 4 5 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 e domain. b) Find an expression for the Fourier coefficients c, Use this expression to find Co,C1,C2,C3,C4,C5 in polar form c) Plot c, and ác, 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) =4, cos(n0 + P,) n=0 e) Take the signal back to the time domain. Write a Fourier series expansion in the form x(1) = £4 cos(n@,t +P„) n=0
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