GTU BE 2020 Summer Question Papers || Gujarat Technological University
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GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER- IV EXAMINATION - SUMMER 2020
Subject Code: 3141005 Date: 27/10/2020
Subject Name: Signal & Systems
Time: 10:30 AM TO 01:00 PM Total Marks: 70
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Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
| Q.1 | Marks | |
|---|---|---|
| (a) | Sketch the following x[n] signal. Also sketch x[n—3] and x[3—n]. x[n]=4u[n+3]-2u[n]—2u[n-3] | 03 |
| (b) | Find whether the following signal is periodic or not? If periodic determine the fundamental period: i x(t) =3cos(t)+4cos(t/6) ii x[n]=1+ ej((4p/7)n + p/2) | 04 |
| (c) | Define: System and determine whether the system y(t) = x(t²) is “Memoryless”, “Linear”, “Time invariant”, “Causal”, “Invertible”. Justify your answers. | 07 |
| Q.2 | ||
| (a) | Explain stability for LTI Systems. Derive the condition of stability for continuous time signal. | 03 |
| (b) | Find discrete Convolution of following pairs of signals. x[n]={1,3,5,7} and h[n]={2,4,6,8} | 04 |
| (c) | For the input x(t) and impulse response h(t) are as shown in Figure - 1, find the output y(t) --- Content provided by FirstRanker.com --- OR Perform the convolution y(t) = x(t) * h(t) , where x(t) and h(t) are as shown in Figure - 2. | 07 |
| Q.3 | ||
| (a) | Explain the trigonometric Fourier series. | 03 |
| (b) | Find Fourier series coefficients of the following signal. x[n]=1+sin((2p/N)n+3cos((2p/N)n+cos((2p/N)n+p/2) | 04 |
| (c) | Find the Fourier series of the periodic signal shown in Figure - 3 --- Content provided by FirstRanker.com --- | 07 |
| Q.4 | ||
| (a) | Determine the Fourier transform of x(t) = e-bt sin(Ot)u(t) where b > 0. | 03 |
| (b) | Enlist frequency shifting and time differentiation properties of Fourier transform. Prove any one of them. | 04 |
| (c) | Consider the Fourier transform X (jO) of a signal shown in Figure - 4. Find the inverse Fourier transform of it. | 07 |
| Q.5 | ||
| (a) | Explain Scaling property in the z -Domain. | 03 |
| (b) | Find the z -transform of x[n] = —u[-n —1]. Also explain ROC. | 04 |
| (c) | If x[n] is a right-handed sequence, determine the inverse z -transform for the function: X(z)= (1+2z-1)/(1-z-1)(1-0.5z-1) OR Explain Differentiation property in the z -Domain. | 07 |
| Q.6 | ||
| (a) | Find the z -transform of the sequence x[n]=u[n]—u[n—5] | 03 |
| (b) | Assuming x[n] to be causal, find the inverse z -transform of the following: H(z)= (2 +2z-1)/(z2 +0.4z-0.12) | 04 |
| (c) | Explain relation between Fourier-transform and z transform using necessary equations. | 07 |
| Q.7 | ||
| (a) | Find the even and odd parts of the following functions. i. x(t)=t u(t+2)—t u(t-1) ii. g(t) =cos(t)+sin(t) + cos(t)sin(t) | 03 |
| (b) | State the sampling theorem. Also explain the reconstruction of a signal from its samples using interpolation. OR Explain sampling theorem and determine the Nyquist rate corresponding the following signal. x(t) =1+ cos(2000pt) +sin(4000pt) | 04 |
| (c) | The following are the impulse responses of discrete-time LTI systems. Determine whether each system is causal and/or stable. Justify your answers. i. h[n]=(5)nu[3-n] A causal LTI system is represented by the following difference equation. y[n]-ay[n-1]=x[n-1] Find the impulse response of the system h[n], as a function of parameter a . | 07 |
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