Download AKTU B-Tech 7th Sem 2016-2017 NME 032NPL 032 Project Management Question Paper

Code: 13A05303

B.Tech II Year I Semester (R13) Supplementary Examinations June 2017

SIGNALS & 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 signals and systems. Classify different types of signals with examples.

   (b) Determine whether the following signals are periodic or not. If periodic, find the fundamental period.

   1. x(t) = cos(t) + sin(v2t)
   2. x(t) = cos(2pt) + sin(5pt)

   OR

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   (a) Explain the following operations on signals with examples:

   1. Time shifting
   2. Time scaling
   3. Time reversal

   (b) Determine whether the following signals are energy or power signals:

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   1. x(t) = e^-atu(t), a > 0
   2. x(t) = Acos(?t)

2. (a) Define linear time-invariant system. Explain the properties of LTI systems.

   (b) Find the convolution of x(t) = e^-2tu(t) and h(t) = u(t+2).

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   OR

   (a) Derive the expression for the transfer function of an LTI system.

   (b) Find the convolution of x(n) = {1, 2, 3} and h(n) = {4, 5, 6, 7}.

3. (a) State and prove the properties of Fourier transform.

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   (b) Find the Fourier transform of x(t) = e^-atu(t), a > 0.

   OR

   (a) Explain the concept of energy spectral density and power spectral density.

   (b) Find the Fourier transform of a rectangular pulse of duration T and amplitude A.

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4. (a) State and prove sampling theorem.

   (b) Explain the concept of aliasing. How can it be avoided?

   OR

   (a) Explain the process of signal reconstruction from its samples.

   (b) What is the Nyquist rate for the signal x(t) = 10cos(20pt)cos(40pt)?

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5. (a) Define Laplace transform. State and prove the properties of Laplace transform.

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

   OR

   (a) Find the inverse Laplace transform of X(s) = 1/(s(s+1)).

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   (b) Explain the concept of region of convergence (ROC) in Laplace transform.

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