Download JNTUH MBA 3rd Sem 2018 Nov Quantitative Analysis for Business Decisions 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

Answer all 5 questions

All questions carry equal marks

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1. a) Define signal and system. Explain the classification of signals with examples.

   b) Consider the signal x(t) shown in the following figure:

   Sketch and label each of the following signals:

   1. x(t-2)
   2. x(2t+1)

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   3. x(-t)

   OR

   a) Explain the concept of orthogonality between two signals. Determine whether the signals x(t) = e^jt and y(t) = e^j2t are orthogonal over the interval 0 ≤ t ≤ 1.

   b) Explain the properties of impulse function.

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

   b) Find the Fourier transform of the following signal:

   x(t) = A -a ≤ t ≤ a

   0 Otherwise

   OR

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   a) Obtain the Fourier transform of a periodic gate function.

   b) Determine the Fourier transform of x(t) = e^-atu(t).

3. a) What is distortion less transmission? Explain the ideal characteristics of an ideal LPF.

   b) What is Hilbert transform? Determine the Hilbert transform of x(t) = cosωt.

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   OR

   a) State and prove the convolution property of Laplace transform.

   b) Find the Laplace transform of f(t) = t²e^-2tu(t).

4. a) Explain the properties of Region of Convergence (ROC) for Laplace transform.

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   b) Determine the inverse Z-transform of:

   X(z) = z / (3z² - 4z + 1), ROC: |z| > 1

   OR

   a) Find the Z-transform of the following:

   i) x(n) = aⁿu(n) ii) x(n) = -bⁿu(-n-1)

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   b) State and prove the time shifting property of Z-transform.

5. a) Define the terms: i) State ii) State variable iii) State vector

   b) Obtain the state transition matrix for the system having

   A = [0 1; -2 -3]

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   OR

   a) Explain the concept of state space representation of continuous time systems.

   b) Find the state transition matrix for the matrix

   A = [0 1; 0 -2]

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