a) If the compact Fourier series of a periodic signal is given by002x(t) =,+6(-1)"sin(пnt)n2n=1Find the power of this signal given thatn490n=1Hint: This is a Parseval's theorem application.b) Explain with reasons, the stability of the LTIC system in terms ofi) BIBO stability, ii) Asymptotic stability, and iii) draw roots on the graph given(D² + 1)(D² + 16)y(t) = (3D + 1)x(t)

Answered: Image /qna-images/answer/4d66aede-cbd2-49dc-a2fd-a979a01b6247.jpg

Answered: a) If the compact Fourier series of a…

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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Consider the periodic signal ?(?) given by the expression x(t) = (2 + 2j)[e^(−j3t)] – 3j[e^(−j2t)] + 5 +3j(e^(j2t) + (2 – 2j)e^(j3t) . a) What is the fundamental frequency of x(t)? b) Find and plot the magnitude and phase of the Fourier series coefficients as a function of frequency. c) Is x(t) a real signal? Why? d) Compute the total power of x(t) using Parseval’s relation.
a. Show that 2-D discrete Fourier Transform of a M × N digital image is periodic.That is, you must prove that F(u + M, v + N) = F(u, v). b. Suggest two methods to bring the frequency origin of a discrete Fourier Transform of an image to the center ofthe 2-D array of frequency plane.
Consider the following discrete time signal periodic with N?[?]=1+sin(2??)?+3cos(2??)?+cos(4???+?2)Find the Fourier series representation of ?[?], i.e. find the Fourier series coefficients ?0, ?−1, ?1, ?−2 and ?2.
The discrete time periodic signal x(n)={2,1,-4,2} has the Fourier coefficients given as ck=(c-8,c-7,c-6,6-j,c-4,c-3,-5,c-1,c0,c1,-5,6-j) .Find the missing coefficients and plot its magnitude spectrum for -8≤k≤3.
a) Make a plot of the normalized fft magnitude as a function of frequency (real frequency in Hz). Only display the frequency range between -1kHz and 1kHz. b) On the same figure as part (c), superimpose the magnitude of the Fourier series coefficients, |??|, as a function of frequency as a stem plot. Again, only display the frequency range between -1kHz and 1kHz. How well do they compare? Hint*: Consider making a frequency vector containing only the Fourier harmonic frequencie
Obtain the Fourier Transform to the rectangular pulse of duration 2 second and having a magnitude of 10 volts.
how to solve fourier series question and concepts ?
Let's examine the function g(t)= {Go for - π < t < -( π/2), {-Go for -( π/2) < t < ( π/2), {Go for ( π/2) < t < π, which is characterized by being 2 π-periodic. Firstly, without mathematical calculations, clarify why every bn value must be 0. Secondly, sketch the g(t) graph within the range of [-4 π,4 π]. Thirdly, express the Fourier expansion of g(t). Lastly, plot the g(t) using the first 3, 5, 10, 15, 20, and 25 terms of the series. At what point does the graph start resembling your initial sketch in the first question?
A power signal depending on time t is written P (t) = P0cos (ωt) cos (ωt), with P0 in watts (W) and t in s (seconds). What are the amplitudes of the non-zero harmonics in the real Fourier spectrum of this signal (i.e. corresponding to the amplitudes an and bn)?Please choose at least one answer:.
A. Consider the two signals whose Fourier Series Spectrum as shown below. Assume that the units of frequency are kiloHertz (kHz). Look at the figure in the picture. What is the Fourier Series Spectrum of the product of these two signals? Pick among the choices. ============================================ B. Suppose that a signal cos⁡(2π⋅10t) modulates a cosinusoidal carrier cos⁡(2π⋅250t), and then mixed with another cosine at the same frequency, i.e. y(t)=cos⁡(2π⋅10t)⋅cos⁡(2π⋅250t)⋅cos⁡(2π⋅250t) Which of the following is an equivalent expression for y(t)? Select one: a. cos⁡(2π⋅510t) b. 0.5cos⁡(2π⋅240t)+0.5cos⁡(2π⋅260t) c. 0.5cos⁡(2π⋅250t)+0.25cos⁡(2π⋅240t)+0.25cos⁡(2π⋅260t) d. 0.5cos⁡(2π⋅10t)+0.25cos⁡(2π⋅490t)+0.25cos⁡(2π⋅510t)
Find the Continuous-Time Fourier Series coefficients for the following continuous-time signal: ?(?) = ? 0 < ? < 4 with a fundamental period of ? = 4
a. Which of the following is true? The Fourier transform of a unit rectangular pulse is A. real. B. not oscillating. C. complex. D. neither real nor complex. b. Which of the following is true? For system and signal operations, the symbol “*” is typically shared between A. convolution and complex conjugate. B. linear combination and complex conjugate. C. orthogonality and complex conjugate. D. multiplication and complex conjugate. c. Which of the following is true? The Fourier transform is based on A. The Fourier series by substituting the signal x(t) into Fourier coefficient’s expression. B. The Fourier series by substituting the Fourier coefficient’s expression into a random signal which is periodic over a defined period. C. The Fourier series by substituting the Fourier coefficient’s expression into x(t). D. The Fourier series because this is a logical process.

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