Download AKTU B-Tech 7th Sem 2016-2017 NEC 703 Vlsi Design Question Paper

ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY & SCIENCES (AUTONOMOUS)

3/4 B. Tech I- Semester Regular Examinations November - 2023

SIGNALS, SYSTEMS AND STOCHASTIC PROCESSES

(Electronics & Communication Engineering)

Date: 27-11-2023 Time: 3 hours Max. Marks: 75

Answer ONE Question from each set All Questions Carry Equal Marks

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SET-I

1. a) Define signal and system. Explain different types of signals with examples. (7 Marks)
   b) Check the following systems for linearity, time-invariance, causality and stability.
   i) y(t) = t x(t)
   ii) y(n) = x(n²) (8 Marks)
   OR

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2. a) Approximate the function f(t) = 1 for 0 < t < 1 by g(t) = At in the least square sense over the interval (0, 1). (7 Marks)
   b) Explain about orthogonal signal space and vector signal. (8 Marks)

SET-II

1. a) State and prove the differentiation and integration properties of Fourier Transform. (7 Marks)
   b) Find the Fourier transform of the Gate function defined by
   f(t) = A for -T/2 < t < T/2
   

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   = 0 Otherwise (8 Marks)
   OR
2. a) Explain the concept of Hilbert Transform. (7 Marks)
   b) Find the inverse Laplace transform of X(s) = 1/(s(s+1)(s+3)) (8 Marks)

SET-III

1. a) Explain the properties of convolution. (7 Marks)
   

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   b) Find the convolution of x(t) = e^-3t u(t) and h(t) = u(t). (8 Marks)
   OR
2. a) State and prove sampling theorem. (7 Marks)
   b) Find the Nyquist rate and Nyquist interval for the signal x(t) = 5 cos 1000pt + 2 sin 500pt (8 Marks)

SET-IV

1. a) Explain the properties of ROC of Laplace transform. (7 Marks)
   

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   b) Find the Z-transform and ROC of x(n) = aⁿ u(n) for a > 0. (8 Marks)
   OR
2. a) Find the inverse Z-transform of X(z) = z/(3z² - 4z + 1) for ROC |z| > 1. (7 Marks)
   b) Find the Discrete Fourier Transform (DFT) of the sequence x(n) = {1, 2, 3, 4}. (8 Marks)

SET-V

1. a) Define Random variable, Random process, Ensemble, Sample function and Probability density function. (7 Marks)
   

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   b) Find the mean and variance of the random variable with density function f_X(x) = a e^{-a x} u(x). (8 Marks)
   OR
2. a) Explain about Gaussian Random process. (7 Marks)
   b) Find the Auto correlation function of the process X(t) = A cos(?t + ?), where A and ? are constants and ? is a uniformly distributed random variable in the interval (0, 2p). (8 Marks)

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