1. Consider a continuous-time periodic signal x(t) = x(t + 7) with Fourier series representationx(t) = [X₂e/2nkt/Tk=-cowhere0.80.6€0.40.2Xk =-12-10Xo = 0.50, k even6л²k²It is straightforward to show that these Fourier series coefficients correspond to a continuous-time periodic trapezoidal signal, plotted below for T = 4 seconds.www2sin-3π/4(πk1sinnk, k odd(a) Suppose another periodic continuous-time signal z(t) is created having Fourier seriescoefficients given by Zx = Xe/. Using the Time Shift property of the continuous-timeFourier Series, sketch z(t), where 7 = 4 seconds.H(n)(b) Suppose the original periodic signal x(t) is input to a continuous-time LTI system withfrequency response H() shown below. With the signal period still T = 4 seconds, find anexpression for the LTI system output signal y(t) and sketch y(t)43m/4(rad/s)1012

Answered: Image /qna-images/answer/2be7c21a-4f45-49e7-b9ff-5d5aeabe96fb.jpg

1. Consider a continuous-time periodic signal x(t) = x(t + 7) with Fourier series representation x(t) = [X₂e/2nkt/T k=-c where 0.8 0.6 € 0.4 Xk = 0.2 Xo = 0.5 0, k even 6 n²k² sin It is straightforward to show that these Fourier series coefficients correspond to a continuous- time periodic trapezoidal signal, plotted below for T = 4 seconds. лky sin nk ,k odd

1. Consider a continuous-time periodic signal x(t) = x(t + 7) with Fourier series representation x(t) = [X₂e/2nkt/T k=-c where 0.8 0.6 € 0.4 Xk = 0.2 Xo = 0.5 0, k even 6 n²k² sin It is straightforward to show that these Fourier series coefficients correspond to a continuous- time periodic trapezoidal signal, plotted below for T = 4 seconds. лky sin nk ,k odd

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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1. Consider the periodic function .x(t) plotted in Figure 1 E -27₁ LES Figure 1: x(t) (a) Compute the Fourier series representation of x(t). 1+2)+1). A new signal is defined as ( 1 ( - (b) Sketch the waveform of y(t) and find its Fourier series coefficients, by, in terms of the Fourier series coefficients,4, of xft).
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M7
subject: Signals, Spectra and Signal Processing
Plz plz solve both.
write the answer in exponetentiol fourier series
If the specific problem does not include instruction in rounding off, express your answer (nonterminating or repeating decimal) using 10 digits as seen in your scientific calculator.
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Just 1a, b and c please
3. Fourier series are the basic mathematical tool of Fourier analysis used to analyze periodic functions through the decomposition of said function into an infinite sum of much simpler sinusoidal functions (as a combination of sines and cosines with integer frequencies). For the graph below, of the half-wave rectified signal, complete the Fourier series, up to the even 10th harmonic.