GTU BE 2020 Summer Question Papers || Gujarat Technological University
Envlmnt No.
GUJARAT TECHNOLOGICAL UNIVERSITY
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BE - SEMESTER- 1V EXAMINATION - SUMMER 2020
Subject Code: 2141005 Date:02/11/2020
Subject Name: SIGNALS AND SYSTEMS
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
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- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
| Marks | |
|---|---|
| Q.1 (a) Based upon nature and characteristics in the time domain, classify signals broadly. In each of the broad domains enlist signals further classification. | 03 |
(b) Sketch each of the following signals.
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(c) Classify following systems as : Causal or non-causal; Linear or nonlinear and Time invariant or time variant
| 07 |
| Q.2 (a) State and prove Linearity property of LTI systems using Laplace transform. | 03 |
| (b) For LTI system, if input sequence is x(n) and impulse response is defined as h(n), derive equation for discrete time convolution sum y(n). | 04 |
| (c) Consider a causal LTI system with impulse response h(t)=e-2tu(t). Find the output of the system for an input x(t)=3.e-t | 07 |
| OR | |
| (c) Solve the following difference equation y(n) +2y(n—1) = x(n) With x(n) = (½)n u(n) and initial condition y(-1)=1 | 07 |
| Q.3 (a) Enlist dirichelts conditions for existence of Fourier transform. | 03 |
| (b) Find discrete time linear convolution of following two sequences using matrices method. x(n)=2d(n+1)-3d(n)+d(n-1)+2d(n-2) h(n)=2d(n-1)+3d(n-2)+4d(n-3) | 04 |
| (c) Compute the Fourier transform for the signal x(t) in following Figure:01 | 07 |
| OR | |
| Q.3 (a) Explain distributive property of LTI systems with suitable figures. | 03 |
| (b) An LTI system has impulse response given by h(n)={2,1,2,1} . Find its response to input x(n)= {1,-2,4}. | 04 |
| (c) Compute the Fourier transform for the signal x(t) in following Figure: 02. | 07 |
| Q.4 (a) Prove that for causal sequences, the ROC of Z transform is exterior of a circle. | 03 |
| (b) Find the Fourier transform of cosine wave cos(?0t). Draw its magnitude spectrum. | 04 |
| (c) State and prove (a) Differentiation in time domain and (b) time shifting properties of LTI systems using Fourier transform. | 07 |
| OR | |
| Q.4 (a) Explain with suitable mathematical equations, relation between Laplace Transform and Fourier Transform. | 03 |
| (b) Using properties of Z transform, compute Z transform for following signals: x(n)=u(-n) x(n)= u(-n-2) | 04 |
| (c) Find fourter transforms of unit impluse function. Define clearly Signam function (sgn(t)) and with its help find FT of unit step function. | 07 |
| Q.5 (a) Find inverse Z transform of X(z)= 2/(3—4z-1+z-2) ; |z| > 1 | 03 |
| (b) Using Z transform, find the convolution of the sequences x1 (n) = {1,2,3,4}; x2 (n) = {1,1,1} | 04 |
| (c) Determine steady state (forced) response for the system with impulse response h(n) = (½)nu(n) for the input x(n) =[cos(pn)u(n) . | 07 |
| OR | |
| Q.5 (a) Find inverse Z transform of | 03 |
| (c) An LTI system is described by the difference equation y(n)—(¾)y(n—1)+(?)y(n—2) = x(n)—(?)x(n—1) Specify the ROC of H(z) and determine h(n) for the following conditions, (1) The system is stable (11) The system is causal | 07 |
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