2 2. Let s[n] be the input to each the three LTI systems with frequency responses shown below.Let cz be the discrete-time Fourier series for s[n]. Remember that we found these in the last class:N=6(3/2, k = 02/3, k =+1k = ±2Ck =0,%3D%3D1/6, k =±3Find an equation and sketch the outputs y1[n], y2[n] and y3[n] from the three systems.H1(ej")1-T/2- TT/2H2(@jw)1-т —Зп/4-7/4T/4Зп /4H3(ej")

Let s[n] be the input to each of the three LTI systems with frequency response shown below. Let ck…

Answered: 2. Let s[n] be the input to each the…

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 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.
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.
Which of the following is not a property of a Fourier Transform? Choices: a.) Modulationb.) Convolutionc.) Frequency Integrald.) Scaling
An analog signal xa(t) has a continuous fourier transform that follows the attached image. If the signal is sampled at 600 samples/sec, the DTFT is the second image. What's the sketch of the spectrum Xa(F) of the origial analog signal?
Consider two discrete signals x1[k] and x2[k]. Let x1[k]; x2[k] be periodic signals with periods N,M respectively. Define y[k] = x1[k] + x2[k]. a) Show that y[k] is periodic with N M. b) Let Fourier coefficients of x1[k] and x2[k] be ak, bk respectively. Find Fourier coefficients ck of y[k] in terms of ak and bk.
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
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1. What does the Fourier series analysis tells us about digital signal? Explain your answer. 2. Explain why digital signals are also prone to attenuation. 3. Does a PCM signal have a smaller bandwidth? Why or Why not? 4. Why digital signals are more immune to noise than analog signals?
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?
The message given in the figure is given as c = 4, b = 3 for the signal m (t). Fourier Transform of the message signal m (t) given in the figure is given as L = 140 Hz in the signal M (f). This message signal is a sinusoidal signal with a carrier frequency of 6000 Hz and amplitude Ac = 1, and frequency modulation with a frequency sensitivity of kf = 0.4 . Calculate the bandwidth of the frequency modulated signal produced according to Carson's rule.
Find the Fourier coefficients c0, c1, c2, c3 for the discrete time signal given as x [n] = [4,5,2,1]. and plot the amplitude and power density spectra for the sign x [n].
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.

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