Download AKTU B-Tech 5th Sem 2016-2017 Power Electronics Nee 502 Question Paper

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

R18 B.Tech II Year II Semester Examinations, November/December - 2020

SIGNALS AND SYSTEMS

(Electronics and Communication Engineering)

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Time: 3 Hours Max. Marks: 75

Note: This question paper contains two parts A and B.

Part A is compulsory which carries 25 marks. Answer all questions in Part A.

Part B consists of 5 Units. Answer any one full question from each unit. Each question carries 10 marks.

PART - A (25 Marks)

1. 1. Define signal and system. Give examples. (2M)

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   2. Define orthogonal signal space. (3M)
   3. State sampling theorem. (2M)
   4. List the properties of ROC of Laplace Transform. (3M)
   5. Define transfer function of a system. (2M)
   6. List the properties of Auto correlation function. (3M)

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   7. Define noise bandwidth. (2M)
   8. Write the relation between bandwidth and rise time. (3M)
   9. Define entropy. (2M)
   10. Define mutual information. (3M)

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PART - B (50 Marks)

(Answer any one full question from each unit)

UNIT - I

2. A continuous time signal x(t) is shown in below figure.

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   Sketch and label carefully each of the following signals:

   1. x(t-1)

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   2. x(2t+1)
   3. x(-t)
   4. x(-2t-2). (10M)

   OR

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3. Determine whether the following signals are periodic or not. If periodic, find the fundamental period.

   1. x(t) = 2 cos(t/4) + cos(t/8)
   2. x(t) = cos(pt) + sin(5pt) (10M)

UNIT - II

4. State and prove properties of Fourier Transform.

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   (10M)

   OR

5. Find the Fourier transform of the gate function defined by

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   x(t) = A for -T/2 < t < T/2

   = 0 otherwise.

   Plot its amplitude spectrum.

   (10M)

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UNIT - III

6. Find the Laplace transform and ROC of the signal x(t) = e^-at u(t) + e^-bt u(-t).

   (10M)

   OR

7. Determine the inverse Laplace transform of

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   X(s) = (s+2) / (s(s+3)) , Re{s} > -3

   (10M)

UNIT - IV

8. Derive the relation between input and output autocorrelation functions of a Linear Time Invariant (LTI) system.

   (10M)

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   OR

9. Find the autocorrelation function of x(t) = A cos(?t).

   (10M)

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UNIT - V

10. Consider a binary symmetric channel with source probabilities P(X = 0) = 0.6, P(X = 1) = 0.4 and channel matrix [0.8 0.2, 0.1 0.9]. Find

    1. P(Y = 0) and P(Y = 1)
    2. P(X = 0, Y = 0) and P(X = 1, Y = 1)
    3. P(X = 0/Y = 0) and P(X = 1/Y = 1) (10M)

    OR

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11. An analog signal is band limited to f_m Hz, is sampled at the Nyquist rate. The samples are quantized into 4 levels. The quantization levels are assumed to be independent and occur with probabilities p1 = p4 = 1/8 and p2 = p3 = 3/8. Find the information rate of the source.

    (10M)

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