GTU BE/B.Tech 2019 Winter Question Papers || Gujarat Technological University
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Envlmnt No.
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER- III (New) EXAMINATION — WINTER 2019
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Subject Code: 3131705 Date: 28/11/2019
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) (1) Define system. (i1) List out the types of system. | 03 |
| (b) Explain convolution property of z-transform. | 04 |
| (c) Consider the RC circuit given in the figure below. Assume that the circuit’s time constant is RC = 1 s. The impulse response of this circuit is given by h(t) = e-tu(t). Determine the voltage across the capacitor, y(t), resulting from an input voltage x(t) = u(t) — u(t-2). | 07 |
| Q.2 (a) Use the convolution property to find the FT of the system output Y(j?) for the following inputs and system impulse response: x(t) = 3e-tu(t) and h(t) = 2e-2tu(t) | 03 |
| (b) Use the convolution property to find the time-domain signal corresponding to the following frequency-domain representation: Y(?) = 1/(1+j?) + 1/(2+j?) | 04 |
| (c) Evaluate the periodic convolution of the sinusoidal signal z(t) = 2 cos(2pt) + sin(4pt) with the periodic square wave x(t) as shown below: --- Content provided by FirstRanker.com --- | 07 |
| OR | |
| (c) The output of an LTI system in response to an input x(t) = e-2tu(t) is y(t) = e-tu(t). Find the frequency response and the impulse response of this system. | 07 |
| Q.3 (a) Find the DTFT of x[n] = d[n] | 03 |
| (b) Find Fourier Series coefficients for the signal defined by x(t) = S d(t — 4t) (summation from t=-8 to 8) | 04 |
| (c) Prove the following properties in context of Continuous Time Fourier Transform: (1) Time shifting (i1) Time and frequency scaling | 07 |
| OR | |
| Q.3 (a) State Dirichlet condition for Fourier series representation. | 03 |
| (b) Prove the duality property of Fourier transform. | 04 |
| (c) Determine the appropriate Fourier representations of the following time domain signals: (1) x(t) = e-tcos(2pt)u(t) (if) x(t) = |sin(2pt)| | 07 |
| Q.4 (a) Explain the linearity property of Laplace transform. | 03 |
| (b) Derive the relationship between Laplace transform and Fourier transform. | 04 |
| (c) Analyze the role of Region of Convergence (ROC) for defining the stability of system in the context of Laplace transform. | 07 |
| OR | |
| Q.4 (a) Explain the modulation property in context of Fourier transform. | 03 |
| (b) Explain the differencing and summation property of discrete Fourier transform. | 04 |
| (c) Find the inverse Discrete Time Fourier Transform (DTFT) of X(ej?) = 1/(1+ ¼e-j? -?e-j2?) | 07 |
| Q.5 (a) Explain the linearity property of z-transform. | 03 |
| (b) Explain the concept of poles-and zeros with respect to z-transform. | 04 |
| (c) Determine the z-transform of the signal x[n]= -(½)nu[-n-1]+ (?)n u[n] Depict the ROC and the locations of poles and zeros of X(z) in the z-plane. | 07 |
| OR | |
| Q.5 (a) Explain the initial value theorem in context of z-transform. | 03 |
| (b) Determine the z-transform of the signal x[n] = anu[n] | 04 |
| (c) Find the inverse z-transform of --- Content provided by FirstRanker.com --- X(z) = 2z2/(z2- 6z + 5)with ROC |z| > 5 | 07 |
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