GTU B.Tech 2020 Winter Question Papers || Gujarat Technological University
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GUJARAT TECHNOLOGICAL UNIVERSITY
BE- SEMESTER-V (NEW) EXAMINATION - WINTER 2020
Subject Code:3150912 Date:01/02/2021
Subject Name:Signals and Systems
Time:10:30 AM TO 12:30 PM Total Marks: 56
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Instructions:
- Attempt any FOUR questions out of EIGHT questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
| Marks | |
|---|---|
| Q.1 (a) Compare Analog Signal and Digital Signal | 03 |
| (b) Differentiate between continuous and discrete time signal. | 04 |
(c) Explain with Example following properties of system.
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| Q.2 (a) Determine the energy and power of a unit step signal. | 03 |
| (b) State and prove the frequency differentiation property of Fourier transform. | 04 |
| (c) Define Laplace transform. Prove linearity property for Laplace transform. State how ROC of Laplace transform is useful in defining stability of systems. | 07 |
| Q.3 (a) Obtain the DFT of unit impulse d(n) | 03 |
| (b) Prove the duality or symmetry property of fourier transform. | 04 |
| (c) Find the fourier transform of the periodic signal x(t)=cos(2pf0t) u(t) | 07 |
| Q.4 (a) State and prove a condition for a discrete time LTI system to be invertible. | 03 |
| (b) State and prove the time scaling property of Laplace transform. | 04 |
| (c) Find the convolution of two signals X1(t) and X2(t) X1(t)= e-2tu(t) X2(t)=u(t-4) | 07 |
| Q.5 (a) State the condition for existence of Fourier integral. | 03 |
| (b) Prove that when a periodic signal is time shifted, then the magnitude of its fourier series coefficient remains unchanged. (|an|=|bn|) | 04 |
| (c) Determine the homogeneous solution of the system described by: y(n) = 3y(n— 1) - 4y(n - 2) = x(n) | 07 |
| Q.6 (a) State and prove the initial value theorem. | 03 |
| (b) State and prove the Final value theorem. | 04 |
| (c) Explain the trigonometric fourier series with suitable example. | 07 |
| Q.7 (a) Explain discrete Fourier transform and enlist its features. | 03 |
| (b) Define the region of convergence with respect to z-transform. | 04 |
| (c) Define: The Z transform. State and prove Time shifting and Time reversal properties of Z transform | 07 |
| Q.8 (a) Determine the z-transform of following finite duration | 03 |
| (b) Calculate two values of x(n) = {1,1,0,1,1}; your answer will | 04 |
(c) Determine if the following systems described by
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