Download VTU B-Tech/B.E 2019 June-July 1st And 2nd Semester 2015 June-July 14MAT21 Engineering Mathematics II Question Paper

Code: 13A05305

B.Tech II Year I Semester (R13) Supplementary Examinations June 2022

SIGNALS AND SYSTEMS

(Common to ECE & EIE)

Time: 3 hours Max. Marks: 70

Answer all 5 questions

All questions carry equal marks

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1. (a) Determine whether the signals are periodic or not. If periodic find the fundamental period.

   1. x(t) = sin(2pt) + cos(3pt)
   2. x(t) = cos(t) + sin(v2t)

   (b) Define and explain the following signals:

   1. Unit impulse

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   2. Unit step
   3. Ramp
   4. Signum

   (OR)

   (a) State and prove properties of Fourier series.

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   (b) Obtain the Fourier series representation of the half wave rectified sine wave.

2. (a) Find the Fourier transform of the signal x(t) = e^-atu(t).

   (b) State and prove the following properties of Fourier transform:

   1. Time shifting

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   2. Frequency shifting

   (OR)

   (a) Find the inverse Fourier transform of X(?) = 2d(?) + d(? - 4) + d(? + 4).

   (b) Explain about energy spectral density and power spectral density.

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3. (a) Define Linear Time Invariant (LTI) system. Explain the properties of LTI system.

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

   (OR)

   (a) Distinguish between:

   1. Causal and Non-causal systems.

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   2. Stable and Unstable systems.

   (b) State and prove the properties of convolution.

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

   (b) Find the Laplace transform of x(t) = t e^-at u(t).

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   (OR)

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

   (b) State and prove initial value and final value theorems.

5. (a) Determine the Z-transform of x(n) = aⁿu(n).

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   (b) State and prove properties of Z-transform.

   (OR)

   (a) Determine the inverse Z-transform of X(z) = z/(3z² - 4z + 1); ROC: |z| > 1.

   (b) Explain the relation between Laplace, Fourier, and Z-transforms.

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