Download AKTU B-Tech 6th Sem 2014-2015 Compiler Design 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 FIVE Questions

All questions carry equal marks

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1. (a) Explain different types of signals with examples.
   (b) Determine whether the following signals are periodic or not. If periodic, determine the fundamental period:
   (i) x(t) = sin(6pt) + cos(12pt)
   (ii) x(t) = cos(t) + sin(v2t)
   (OR)
   

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   (a) Discuss about various elementary signals.
   (b) Determine whether the system described by the equation y(t) = x(t) + tx(t) is: (i) Linear (ii) Time-invariant (iii) Causal (iv) Stable.
2. (a) State and prove the following properties of Fourier Transform:
   (i) Time shifting property
   (ii) Frequency shifting property
   

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   (b) Find the Fourier transform of the gate function defined by: x(t) = A for |t| < T/2 and x(t) = 0 for |t| > T/2.
   (OR)
   (a) Explain the concept of signal transmission through a linear system.
   (b) Find the Fourier transform of x(t) = e^-atu(t), a > 0.
3. (a) Define the term 'energy spectral density' and 'power spectral density'. Explain how these are useful in signal analysis.
   

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   (b) Find the autocorrelation function of x(t) = Acos(?t).
   (OR)
   (a) Explain the relationship between autocorrelation and power spectral density.
   (b) Find the energy spectral density of x(t) = e^-atu(t).
4. (a) State and prove the sampling theorem for band-limited signals.
   

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   (b) Explain the concept of aliasing.
   (OR)
   (a) Explain the reconstruction of the signal from its samples.
   (b) What is the effect of under sampling? Explain.
5. (a) Explain properties of Region of Convergence (ROC) of Laplace transform.
   

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   (b) Find the Laplace transform of x(t) = e^-atu(t) and specify its ROC.
   (OR)
   (a) Find the inverse Laplace transform of X(s) = 1/(s+1)(s+2).
   (b) Discuss about the relation between Laplace transform and Fourier transform.

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