GTU BE 2020 Summer Question Papers || Gujarat Technological University
Envlmnt No.
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER- III EXAMINATION - SUMMER 2020
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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:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
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| 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.
| 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.
--- Content provided by FirstRanker.com --- | 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 ?0t+2cos?0t+cos[2?0t+p/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.
| 07 |
| Q.4 (a) Explain time reversal and linearity property for the discrete time Fourier transforms. | 03 |
| (b) Determine the Fourier transform for -p < ? < p for the periodic signal x(n) = sin(p/4n + p/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(6pt + p/8) | 04 |
(c) Compute the Fourier transform of each of the following signals:
--- 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)
| 07 |
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