Download AKTU B-Tech 5th Sem 2015-2016 Fundametals Of E.M. Theory Eec 508 Question Paper

Code: 13A05305

B.Tech II Year I Semester (R13) Regular Examinations December 2014

SIGNALS AND SYSTEMS

(Common to ECE and EIE)

Time: 3 hours Max. Marks: 70

Note: Question paper consists of Two parts (Part-A and Part-B)

Answer all questions in Part-A and any three questions from Part-B

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PART-A (22 Marks)

1. (a) Define signal and system. Give examples. (2M)
   (b) Determine whether the signals are periodic or not. If periodic, find the fundamental period. (3M)
   (i) x(t) = cos(t) + sin(v2t)
   (ii) x[n] = cos(pn/2) + cos(pn/4)

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2. Define and write properties of Fourier transform. (3M)

3. What is aliasing? Explain how to overcome the effect of aliasing. (3M)

4. What is Hilbert transform? Mention its properties. (3M)

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5. Define Z-transform and ROC. (3M)

6. List the properties of the ROC of Z-transform. (5M)

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PART-B (3 x 16 = 48 Marks)

1. (a) Consider the signal x(t) = d(t+2) - d(t-2). Evaluate ?⁸_-8 x(t)dt. (8M)
   (b) Check the following systems for linearity, causality and time invariance.
   (i) y(t) = x²(t)
   (ii) y(n) = x(-n) (8M)

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2. (a) State and prove properties of convolution. (8M)
   (b) Find the Fourier transform of the signal x(t) = e^-atu(t). (8M)

3. (a) Explain sampling theorem for band limited signals. (8M)
   (b) Find the Nyquist rate and Nyquist interval for the signal x(t) = sin(500pt) + cos(1000pt). (8M)

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4. (a) Find the Laplace transform of the signal x(t) = te^-atu(t). (8M)
   (b) Determine the inverse Laplace transform of X(s) = 1/(s² + 3s + 2) , ROC: -2 < Re{s} < -1. (8M)

5. (a) Find the Z-transform of x(n) = n²u(n). (8M)
   

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   (b) Find the inverse Z-transform of X(z) = z/(z-1)(z-2), ROC: |z| > 2. (8M)

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