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Fourier Series Consider the following signal: x(t) =1+sin 2t + sin(3t +x / 6) a) Check that the signal is periodic. Find the fundamental period and frequency T and w , Convert the given signal to the 0 domain, where 0 is the electric angle. What harmonics are present in this signal? b) Using the matching coefficient technique find the Fourier complex coefficients c, expressed in polar form. Tabulate these coefficients for n2 0. Plot the coefficients in magnitude and phase for n20 as well as for n<0. c) From reading the above plot, write x(0) as a DC component plus a summation of harmonics. Finally, convert your answer to the time domain.

Fourier Series Consider the following signal: x(t) =1+sin 2t + sin(3t +x / 6) a) Check that the signal is periodic. Find the fundamental period and frequency T and w , Convert the given signal to the 0 domain, where 0 is the electric angle. What harmonics are present in this signal? b) Using the matching coefficient technique find the Fourier complex coefficients c, expressed in polar form. Tabulate these coefficients for n2 0. Plot the coefficients in magnitude and phase for n20 as well as for n<0. c) From reading the above plot, write x(0) as a DC component plus a summation of harmonics. Finally, convert your answer to the time domain.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Please help solve the question shown in the photo. There is only 1 problem, but it has three parts to it. I want to know how to solve all parts completely so please show all steps clearly. Thank you.

### Fourier Series Consider the following signal: \[ x(t) = 1 + \sin 2t + \sin(3t + \pi/6) \] #### Questions **a)** - Check that the signal is periodic. - Find the fundamental period and frequency \( T_f \) and \( \omega_1 \). - Convert the given signal to the \( \theta \) domain, where \( \theta \) is the electric angle. - What harmonics are present in this signal? **b)** - Using the matching coefficient technique, find the Fourier complex coefficients \( c_n \) expressed in polar form. - Tabulate these coefficients for \( n \geq 0 \). - Plot the coefficients in magnitude and phase for \( n \geq 0 \) as well as for \( n < 0 \). **c)** - From reading the above plot, write \( x(\theta) \) as a DC component plus a summation of harmonics. - Finally, convert your answer to the time domain.
Transcribed Image Text:### Fourier Series Consider the following signal: \[ x(t) = 1 + \sin 2t + \sin(3t + \pi/6) \] #### Questions **a)** - Check that the signal is periodic. - Find the fundamental period and frequency \( T_f \) and \( \omega_1 \). - Convert the given signal to the \( \theta \) domain, where \( \theta \) is the electric angle. - What harmonics are present in this signal? **b)** - Using the matching coefficient technique, find the Fourier complex coefficients \( c_n \) expressed in polar form. - Tabulate these coefficients for \( n \geq 0 \). - Plot the coefficients in magnitude and phase for \( n \geq 0 \) as well as for \( n < 0 \). **c)** - From reading the above plot, write \( x(\theta) \) as a DC component plus a summation of harmonics. - Finally, convert your answer to the time domain.
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