Download VTU B-Tech/B.E 2019 June-July 1st And 2nd Semester 17 Scheme 17PHY12 Engineering Physics Question Paper

Code: 13A05305

B.Tech II Year I Semester (R13) Supplementary Examinations June 2022

SIGNALS AND SYSTEMS

(Common to ECE and EIE)

Time: 3 hours Max. Marks: 70

Note: Answer all Questions. Assume missing data, if any.

PART - A

(22 Marks)

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1. Answer the following:

   1. Define signal and system. Explain different types of signals with examples.

   2. State and prove the time shifting and time scaling properties of Fourier Transform.

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   3. Define an LTI system. Explain how it is characterized by its impulse response.

   4. Define ROC. List the properties of ROC for Laplace Transform.

   5. What is aliasing? How can it be avoided?

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   6. State and prove initial value and final value theorems of Z-transform.

PART - B

(4 x 12 = 48 Marks)

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Answer all questions. Each question carries 12 marks.

2. (a) Determine whether the following signals are periodic or not. If periodic, find the fundamental period.
   (i) x(t) = cos(2t) + sin(3t)
   (ii) x(t) = cos(2pt) + sin(3pt)

   (b) Find the exponential Fourier series for the signal x(t) = A cos(?₀t).

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   OR

   (a) Explain the properties of the Hilbert transform.

   (b) Find the Fourier transform of the signum function.

3. (a) State and prove sampling theorem for band limited signals.

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   (b) Find the convolution of the signals x(t) = e^-tu(t) and h(t) = u(t).

   OR

   (a) Determine the transfer function and impulse response of a LTI system described by the differential equation: dy(t)/dt + 2y(t) = x(t)

   (b) State and prove Parseval's theorem for continuous time signals.

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4. (a) Find the Laplace transform of the following signals:
   (i) x(t) = t e^-atu(t) (ii) x(t) = sin(?t) u(t)

   (b) Find the inverse Laplace transform of X(s) = (s+2) / (s² + 5s + 6)

   OR

   (a) Determine the transfer function and impulse response of a causal LTI system described by the differential equation: d²y(t)/dt² + 5dy(t)/dt + 6y(t) = dx(t)/dt + x(t)

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   (b) Explain the properties of Laplace Transform.

5. (a) Find the Z-transform of the following signals:
   (i) x(n) = aⁿu(n) (ii) x(n) = n aⁿu(n)

   (b) Find the inverse Z-transform of X(z) = z / ((z-1)(z-2)), ROC: |z| > 2

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   OR

   (a) Determine the transfer function and impulse response of a causal LTI system described by the difference equation: y(n) - (3/4)y(n-1) + (1/8)y(n-2) = x(n)

   (b) Explain the properties of Z-transform.

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