helllp 7- Take a system H such that its frequency response in the frequency range of [−π π],is5,H(e) =5,for w≤for 子,0,Otherwise.a) Sketch the frequency response of the system. Can you express this frequency re-sponse as the difference of two low-pass filters with two differenet cut-off frequencies?b) Find the impulse response h(n), of this system.c) Find the output, if the following signal is applied as the input to the systemx(n) = 2 cos(0.4πn) - 3sin(2.1лn) + cos(πn).d) Is this system realizable?(You may assume that for a low-pass filter F, with the cut-off freq. We, the impulseresponse is given as, ƒ(n) = sin(n) when n0, and f(0) = s.)7771

Answered: Image /qna-images/answer/7878296a-6677-43a1-9e96-b7f18a82f388.jpg

Answered: 7- Take a system H such that its…

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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Let the impulse response of a filter be ℎ[?] = {ℎ[0] = −0.5, 0.5}a) Calculate the frequency response ?(???). Is it a low-pass or a high-pass filter? Plot boththe magnitude and phase responses.b) Obtain the I/O relation for this filter.c) Is this a causal filter? Explain your answer.
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Problem 2 Each of the following figures shows the impulse response of a LTI system h[n]. For each figure in (a), (b), (c) and (d): (i) Firstly write an expression of h[n] and then find an expression of the frequency response of the system: h[n]e-inw (ii) say whether H(e) as a function of w is even or odd or neither (iii) and sketch/plot the magnitude of the frequency response, i.e., H(ew)|, over -27 < w 2π (you may use Matlab). (a) (b) In each figure, the value indicated for each impulse means the amplitude of that impulse. For example, if the value of an impulse at n = 3 is indicated to be 2j, it means 2jd[n – 3]. The value of h[n] is zero for all n outside the range shown in the figure. h[n] (c) H(ejw) = h[n] 1 1 1 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 h[n] -6 -5 -4 -3 -2 -1 0 1 -6-5-4-3-2-1 0 1 n=-∞ 1 1 1 1 1 2 3 4 5 6 2 3 4 5 6 n n h[n] is real-valued. h[n] is real-valued. h[n] is real-valued.
Q1: For the pole-zero diagram shown in Figure below, the lengths of poles and zeros from the origin are 0.5 and 0.8 respectively: a. Find the transfer function H(z), impulse response h(n) and the difference equation. b. Calculate and plot the magnitude and phase frequency responses. Im(z) Re(z)
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Problem 5 For the difference equation 0=2y[n+2]-3y[n+1]-2y[n]-4x[n+2]+2x[n+1] a. Put the difference equation in standard causal form_y[n]=... b. Draw a block diagram (i.e., flow diagram, or digital filter structure) implementing this difference equation. c. For the input x[n] = [n] and the system at rest (i.e., zero initial conditions), compute y[-1],y[0], y[1],y[2], and y[3] by hand directly from the difference equation. d. Find the transfer function H(z). e. Compute the unit pulse response h[n],via inverse z-transform. Confirm that [-1] through h[3] are identical to the samples of the unit pulse response computed above via direct iteration of the difference equation.
1. Consider the following Lowpass Filter System. R V„(t) i(t) out (a) Find the differential equation for the system. Assume that Vout (0) = 0 (b) When R=1M9, c=1F, and Vin (t) = 1 (t) volt (i.e. unit step input). By solving the differential equation, find the response of i(t). Also find the response of Vous (t) (c) We define RC=T as the time constant of the system. For various values of 7 (i.e, T=0.1, 7=1 and T= 10), plot the responses of Vout (t) using MATLAB.
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Ex. 600. A series circuit containing a resitor (6 Ohms), a capacitor (4 Farads), inductor (13 Henries), and a voltage source V. Determine the transfer function I(s)/V(s) and then determine the undamped natural frequency (Wn) and damping ratio (zeta). Answers: Wn, and zeta. ans:2

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