GTU BE/B.Tech 2019 Winter Question Papers || Gujarat Technological University
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER- IV (New) EXAMINATION - WINTER 2019
--- Content provided by FirstRanker.com ---
Subject Code: 2141005 Date: 17/12/2019
Subject Name: Signals and Systems
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
--- Content provided by FirstRanker.com ---
| MARKS | ||
| Q.1 (a) | Consider an analog pulse | 03 |
| x(t) = { 1 0 < t < 1 0 Otherwise | ||
| Find mathematical expression for x (t)delayed by 2, advanced by 2, and the reflected signal x(—t). | ||
| (b) | Determine whether or not the following signals is periodic. If a signal is periodic, determine its fundamental period. | 04 |
| i x(t) = cost + sinv2t | ||
| ii. x[n] = G | ||
| (c) | Evaluate y[n] = x[n] * h[n], by graphical method. where x[n] and h[n] are shown figure below. | 07 |
| x[n] h[n] | ||
| 0 1 2 3 n 0 0 1 2 n | ||
| Q.2 (a) | Determine the energy and power of a unit step signal. | 03 |
| (b) | Consider a discrete-time LTI system with impulse response h[n] given by h[n] = anu[n] | 04 |
| i. Is this system causal? | ||
| 11. Is this system BIBO stable? | ||
| (c) | Determine natural response of the first order system governed by the equation, | 07 |
| dy(t)/dt +3y(t) = x(t); y(0) = 2 | ||
| OR | ||
| Take, h1(t) = tu(t); h2(t) = 3u(t); h3(t) = 2u(t); | ||
| h4(t) = ... | ||
| h5(t) = ... | ||
| Q.3 (a) | Find the Laplace transform of x(t) = sin2t. | 03 |
| (b) | Determine the complex exponential Fourier series representation for the signals x(t) = cos (2t + f) | 04 |
| (c) | Determine the trigonometric Fourier series of periodic impulse train | 07 |
| ? ?(t-kT0) from k=-8 to 8 | ||
| OR | ||
| Q.3 (a) | State and prove the frequency differentiation property of Fourier transform. | 03 |
| (b) | Find the Fourier transform of x(n)={4, 2, 1, 2} | 04 |
| (c) | Determine the frequency response of the LTI system defined by, y(n)=x(n) + by(n—1) | 07 |
| Q.4 (a) | Determine the z-transform of x(n) = (n— 3)u(n) | 03 |
| (b) | State and prove shifting property for one sided z-transform. | 04 |
| (c) | Determine the inverse z-transform of X(z) = 1/(z-0.6) for ROC, |z| > 0.6. | 07 |
| OR | ||
| Q.4 (a) | Find the even part of signal x(n) = u(n) + u(—n). | 03 |
| (b) | Determine the inverse z-transform of X(2) =log(1+az-1) ; |z| > |a|. | 04 |
| (c) | Determine the impulse response h(n) for the system described by the second order difference equation, y(n) —4y(n-1)+4y(n-2)=x(n-1) | 07 |
| Q.5 (a) | Test the following systems for linearity. y(t) = 4x(t) + 258, | 03 |
| (b) | State and prove the time scaling property of Laplace transform. | 04 |
| (c) | A system has impulse response h(n) given by, | 07 |
| h(n) = (1/4)nu(n) | ||
| 1. Is the system BIBO stable? | ||
| 11. Is the system causal? Justify your answer. | ||
| OR | ||
| Q.5 (a) | 1. Define Fourier transform. | 03 |
| 11. State the condition for existence of Fourier integral. | ||
| (b) | Calculate the DFT of the sequence, x(n) ={1,1,-2,-2} | 04 |
| (c) | Define ROC for z-transform. List the property of ROC. | 07 |
--- Content provided by FirstRanker.com ---
This download link is referred from the post: GTU BE/B.Tech 2019 Winter Question Papers || Gujarat Technological University