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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 FIVE Questions

All questions carry equal marks

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1. a) Define signal and system. Explain about elementary signals.

   b) Check whether the following systems are static or dynamic, causal or non-causal, linear or non-linear, time variant or time invariant.

   1. y(t) = x(t) + 3
   2. y(t) = x(t²)

   (OR)

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2. a) Explain the concept of orthogonality between two signals f₁(t) and f₂(t).

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

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

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3. a) State and prove differentiation and integration properties of Fourier Transform.

   b) Find the Fourier transform of the signal x(t) = e^-atu(t)

   (OR)

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4. a) Define Hilbert transform and mention its properties.

   b) Find the Fourier transform of signum function.

5. a) Define system bandwidth and signal bandwidth.

   b) What is distortion less transmission through a system? Explain.

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   (OR)

6. a) Explain the relationship between bandwidth and rise time.

   b) Obtain the conditions for the physical realizability of LTI system.

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7. a) What is noise bandwidth? Derive the expression for noise bandwidth.

   b) Find the autocorrelation function of x(t) = Acos(?t + ?).

   (OR)

8. a) Define cross correlation and write its properties.

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   b) Find the cross correlation between x(t) = e^-tu(t) and y(t) = e^-2tu(t)

9. a) Explain about sampling theorem.

   b) Discuss about different types of sampling techniques.

   (OR)

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10. a) Explain the reconstruction of signal from its samples.

    b) Write short notes on Aliasing.

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