Download AKTU B-Tech 7th Sem 2015-2016 ECS 077 Data Compression Question Paper

Code: 20A3301

B.Tech II Year I Semester (R20) Regular Examinations November 2021

SIGNALS AND SYSTEMS

(Electrical and Electronics Engineering)

Time: 3 Hours Max. Marks: 70

Note: 1. Question paper consists of two parts i.e., Part A and Part B.

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PART – A (10 * 2 = 20 Marks)

1. a) Define signal and system.
2. b) Find the Fourier series coefficients of x(t) = cos ?₀t.
3. c) State Dirichlet's conditions for existence of Fourier Transform.

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4. d) Define Energy Spectral Density (ESD) and Power Spectral Density (PSD).
5. e) Define linear time invariant (LTI) system.
6. f) List the properties of convolution.
7. g) Define ROC of Laplace transform.
8. h) Find the Laplace transform of x(t) = e^-at u(t).

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9. i) Define Z-transform.
10. j) List the properties of Z-transform.

PART – B (5 * 10 = 50 Marks)

Unit-I

1. a) Discuss the concept of orthogonality between two signals f₁(t) and f₂(t).
   (5 Marks)
   

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   b) Determine whether the signal x(t) = cos(3t) + sin²(2t) is periodic or not. If periodic, determine its fundamental period.
   (5 Marks)
2. OR
3. a) Approximate the function f(t) = t, 0 < t < 1 by g(t) = c sin(pt) using the principle of orthogonality.
   (5 Marks)
   

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   b) Explain about various elementary signals.
   (5 Marks)

Unit-II

1. a) Find the Fourier series representation of the signal x(t) = A cos(?₀t).
   (5 Marks)
   

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   b) State and prove time scaling property of Fourier transform.
   (5 Marks)
2. OR
3. a) State and prove differentiation in time domain property of Fourier transform.
   (5 Marks)
   

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   b) Find the Fourier transform of the gate function x(t) = 1, -T/2 < t < T/2.
   (5 Marks)

Unit-III

1. a) Derive the relation between input and output of an LTI system.
   (5 Marks)
   

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   b) Find the convolution of x(t) = e^-2t u(t) and h(t) = u(t).
   (5 Marks)
2. OR
3. a) Define causality and stability of LTI system.
   (5 Marks)
   

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   b) Obtain the condition for distortionless transmission through a system.
   (5 Marks)

Unit-IV

1. a) State and prove time shifting property of Laplace transform.
   (5 Marks)
   

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   b) Find the Laplace transform of x(t) = t e^-at u(t).
   (5 Marks)
2. OR
3. a) Determine the inverse Laplace transform of X(s) = 1/(s+1)(s+2) with ROC -2 < Re{s} < -1.
   (5 Marks)
   

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   b) The system transfer function is given by H(s) = s/(s² + 5s + 6). Determine the impulse response.
   (5 Marks)

Unit-V

1. a) State and prove time shifting property of Z-transform.
   (5 Marks)
   

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   b) Find the Z-transform of x(n) = aⁿ u(n).
   (5 Marks)
2. OR
3. a) Determine the inverse Z-transform of X(z) = z/(z-1)(z-2) with ROC |z| > 2.
   (5 Marks)
   

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   b) Explain about the relation between Laplace transform and Z-transform.
   (5 Marks)

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