8. We want to design a causal discrete-time LTI system with the property thatп-1if the input is x(n) = ;) u(n) - u(n – 1)Then the output is y(n) = () u(n)Determine the impulse response h(n) and the system function H(z).9. Consider the causal systemУ(т) %3D —а1у(п - 1) + box(п) + b1x(п — 1)Determine:(a) The impulse response(b) The step response(d) The response to the input x(n) = cos(won) 0

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8. We want to design a causal discrete-time LTI system with the property that if the input is x(n) ==)" u(n) -E) 2) -G)u(n – 1) Then the output is y(n) = () u(n) Determine the impulse response h(n) and the system function H(z).

8. We want to design a causal discrete-time LTI system with the property that if the input is x(n) ==)" u(n) -E) 2) -G)u(n – 1) Then the output is y(n) = () u(n) Determine the impulse response h(n) and the system function H(z).

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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The impulse response of a linear phase FIR and LTI system is given as h[n]={2, -1, 3, -1, 2}.a) Calculate the frequency response of the system with DFT. Give the amplitude and phase responses and the group delay.b) Let h'[n]={ 2, -1, 3, -1, 2, 0} be the periodic state of h[n] with N=6. Give the DFS coefficients of h'[n]. Compare the computational load for DFT and FFT algorithms.c) The input sign x[n]={1, 2} is applied to the system in (a). Calculate the 5-point circular convolution of x[n] and h[n]: c[n] = x[n] ⊗ 5 h[n]d) Now calculate the output y[n] of the system first by linear convolution: y1[n] = x[n] * h[n], then by circular convolution: y2[n] = x[n] ⊗ h [n]. Compare the results.
y[n]+1.2y[n-1]+0.2y[n-2]=x[n]-0.5x[n-1] x[n] is system's input, y[n] is system's output. a) Find the transfer function of the system, H(z). Show the region of convergence by drawing the zero-pole diagram. b) Draw the block diagram representation of the system. c) Find h[n], which is the impulse response of the system. d) Is the frequency response H(e^jw) defined for this system? H(e^jw) if defined?
Measurements conducted on a servomechanism show the system response to be: C (t) = 0.3 e 60t + 1.5 e 10t, when subjected to a unit step input. [1].Obtain the expression for the closed-loop transfer function. [2].Determine the undamped natural frequency and damping ratio of the system.
The impulse response of an LTI system is h(n) = 3δ(n) + (1/4)n u(n). Find the frequency response, H(e jω), and the difference equation of this system. An input signal x(n) = (1/3)n u(n), is applied to this system and an output signal y(n) is observed. Find the output signal, y(n), using DTFT methods. Give the system function H(z) using the frequency response H(ejω). Find the zeros, poles and ROC of this system and show them on the complex plane. Discuss the stability, causality, FIR/IIR and memory properties of this system.
y[z]=6cos2(pi×z/4)a.The above equation shows a discrete time signal, y[z] from a device, determine the four point DFT of the sequence.H(ejw) = {1, 0≤|w|≤wC {0, WC |W|< π b.The expression above shows the DTFT of a lowpass filter system. In order to get the impulse response h[n], determine the inverse DTFT of the system
The transfer function is H(s) = (1.2s+0.18)/(s3 + 0.74s2 + 0.92s) and C(s) = (K(s+1))/ s A) A disturbance input W(s) =W/sk , where W is a constant, into the feedbackcontroller as shown below. We set R(s) = 0. What type of disturbance input W(s)(step, ramp, or parabola) can thesystem reject (i.e., the steady-state error ess is a nonzero constant)? (B) Suppose you want to design the controller C(s) to produce a closed-loop response to areference step input that has no more than 30% maximum overshoot (Mp ≤ 0.30) and a peak timeof no more than 8 sec (tp ≤ 8). Given the specifications on Mp and tp , compute the constraintson the damping ratio ζ and the damped natural frequency ω, assuming that the closed-loop systemis approximated as a 2nd-order underdamped system. Sketch the allowable regions in thecomplex plane (the s-plane) that these constraints define, and shade in the regions where the polesshould not be placed.
3. A causal discrete-time LTI system is described by y[x] -ln - 1] +ln – 2] = x[n] where x[n] and y[n] are the input and output of the system, respectively (a) Determine system transfer function H(2) (b) Find the impulse response h[n] of the system.
Consider a DT LTI system with impulse response h[n] = 2e0.2n , for n = 0, 1, 2,.... What isits output y[n] excited by the input u[n]? Compute y[n] for n = 0 : 3 if u[n] = 1/(n + 1) forn = 0, 1, 2,...
A stable x(n) input signal is applied to an LTI system with a unit impulse response h(n), and y(n)=2 (1/4)'' u(n) output is obtained. a) Find the frequency response,H(ejω), of the system. b) Find the x(n) sign and spectrum applied to the input by DTFT. c) Give the input/output differential equation of the system.
A Discrete time LTI system with impulse response h[n]={1,2,-1} accepts the input x[n]={1, -a+1, 2-a, 3-a, 4+a, 5-a, 4-a, 3+a}to generate the output y[n]. Determine the output of the LTI System using Overlap save convolution. (Hint: a=8)Model Short Answery1(n)=(1,2,3,4,5,6)y2(n)=(7,8,9,10,11,12)y(n)=(8,9,10,11,12,13,14)
An LTI system’s input-output relation is described by y(n) = 0.8y(n−1) + 2x(n−1).(a) Find the impulse response of the system for n = 0, 1, 2, 3, 4 by inputting aunit impulse input.(b) Find the transfer function H(z) of the system.(c) Find the expression of the impulse response h(n).
The impulse response of a linear phase FIR and LTI system is given as h(n)={1, -1/2, 2, -1/2, 1}.a) Calculate the frequency response of the system with DFT. Give the amplitude and phase responses and the group delay.b) Let h'(n)={1, -1/2, 2, -1/2, 1, 0} be the periodic form of h(n) with N=6. Give the DFS coefficients of h'(n). Compare the computational load for DFT and FFT algorithms. (The calculation load for DFT is N2,For FFT, N is calculated as log2 N)c) The input sign x(n)={1, 2} is applied to the system in (a). Calculate the 5-point circular convolution of x(n) and h(n) in the time or frequency domain: c(n) = x(n) *5 h(n)d) Now calculate the output y(n) of the system first by linear convolution: y1(n) = x(n) * h(n), then by circular convolution of 6 points, in the time or frequency domain: y2(n) = x(n) *6 h(n). Compare the results.