FirstRanker Logo

FirstRanker.com - FirstRanker's Choice is a hub of Question Papers & Study Materials for B-Tech, B.E, M-Tech, MCA, M.Sc, MBBS, BDS, MBA, B.Sc, Degree, B.Sc Nursing, B-Pharmacy, D-Pharmacy, MD, Medical, Dental, Engineering students. All services of FirstRanker.com are FREE

📱

Get the MBBS Question Bank Android App

Access previous years' papers, solved question papers, notes, and more on the go!

Install From Play Store

Download GTU B.Tech 2020 Summer 3rd Sem 3131705 Dynamics Of Linear Systems Question Paper

Download GTU (Gujarat Technological University Ahmedabad) B.Tech/BE (Bachelor of Technology/ Bachelor of Engineering) 2020 Summer 3rd Sem 3131705 Dynamics Of Linear Systems Previous Question Paper

This post was last modified on 04 March 2021

This download link is referred from the post: GTU BE 2020 Summer Question Papers || Gujarat Technological University


Envlmnt No.

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER- III EXAMINATION - SUMMER 2020

--- Content provided by FirstRanker.com ---

Subject Code: 3131705 Date: 27/10/2020

Subject Name: Dynamics of Linear Systems

Time: 02:30 PM TO 05:00 PM Total Marks: 70

Instructions:

  1. Attempt all questions.
  2. --- Content provided by FirstRanker.com ---

  3. Make suitable assumptions wherever necessary.
  4. Figures to the right indicate full marks.
Marks
Q.1 (a) Explain continuous-time and discrete-time signals with suitable example. 03
(b) For each of the following input-output relationships, determine whether the corresponding system is linear, time invariant or both.
  1. y(t)=x(t-1)
  2. y[n]=x[n+ 1] -x[n- 1]
04
(c) What is time-variant and time-invariant system? Determine causality and stability of the following discrete-time systems with justification. Consider y[n] is the system output and x[n] is the system input.
  1. y[n]=x[-n]
  2. --- Content provided by FirstRanker.com ---

  3. y[n]=x[n-2]-2x[n- 8]
07
Q.2 (a) Explain LTI systems with and without memory. 03
(b) A linear time-invariant system is characterized by its impulse response A[n]= (1/4) u(n). Determine energy density spectrum of the output signal when the system is excited by the signal x[n]= (1/7) u(n). 04
(c) Compute and plot the convolution y[n] = x[n] * h[n], where x[n]= (1/3)n and h[n] = u[n-1]. 07
OR
(c) Explain commutative and distributive property of a LTI system. 07
Q.3 (a) For x(t) =1+sin ω0t+2cosω0t+cos[2ω0t+π/4] Determine Fourier series coefficient using complex exponential representation. 03
(b) Discuss applications of frequency-selective filters. 04
(c) Discuss the properties of continuous-time Fourier series. 07
OR
Q.3 (a) Each of the two sequences x1[n] and x2[n] has a period N = 4, and the corresponding Fourier series coefficients are specified as x1[n] <—> ak and x2[n] <—> bk Where, a0=a1 =a2=a3=1 and b0=b1=b2=b3=1. Using the multiplication property, determine the Fourier series coefficients ck for the signal g[n] = x1[n] x2[n]. 03
(b) Discuss applications of frequency-shaping filters. 04
(c) Determine whether each of the following statements is true or false. Justify your answers.
  1. An odd and imaginary signal always has an odd and imaginary Fourier transform.
  2. The convolution of an odd Fourier transform with an even Fourier transform is always odd.
07
Q.4 (a) Explain time reversal and linearity property for the discrete time Fourier transforms. 03
(b) Determine the Fourier transform for -π < ω < π for the periodic signal x(n) = sin(π/4n + π/8) 04
(c) Consider a discrete-time LTI system with impulse response h(n) = (1/2) u(n). Use Fourier transforms to determine the response for the input x(n)=(1/3)n u(n). 07
OR
Q.4 (a) Explain differentiation and integration property for the continuous time Fourier transforms. 03
(b) Determine the Fourier transform of periodic signal x(t)=1+ cos(6πt + π/8) 04
(c) Compute the Fourier transform of each of the following signals:
  1. x[n]=u[n-2]-u[n-6]
  2. x[n]= (1/5)nu[-n -1]
  3. --- Content provided by FirstRanker.com ---

07
Q.5 (a) Determine the Laplace transform and the associated region of convergence for x(t) = e-2t u(t) +e-3t u(t). 03
(b) Determine the function of time x(t), for the following Laplace transforms and their associated regions of convergence:
1/s+9 , Re{s}>0.
04
(c) Explain properties of the Z-transform. 07
OR
Q.5 (a) Find Z-transform and region of convergence of x(n) = 1/7(1/3)n u(n)- 1/6(1/5)n u(n). 03
(b) Find inverse Z-transform for X(z) = log(1+az-1), |z|>|a|. 04
(c) Consider the system function corresponding to causal LTI systems: H(z)= 1/(1-1/2z-1 +1/3z-2)(1-1/4z-1 +1/8z-2)
  1. Draw a direct-form block diagram.
  2. Draw a block diagram that corresponds to the cascade connection of two second-order block diagrams. Each second-order block diagram should be in direct form.
07

FirstRanker.com


--- Content provided by FirstRanker.com ---


This download link is referred from the post: GTU BE 2020 Summer Question Papers || Gujarat Technological University