Download AKTU B-Tech 5th Sem 2016-2017 Principles Of Programming Language Ncs 503 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) Define signal and system. Explain the classification of signals with examples.
   (b) Check whether the following systems are static or dynamic, causal or non-causal, linear or non-linear, and time-variant or time-invariant:
   (i) y(t) = x(t) + tx(t-2)
   (ii) y(n) = x²(n)
   (OR)

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2. (a) Explain about elementary signals.
   (b) Find the even and odd components of the following signals:
   (i) x(t) = t cos(t) + t² sin(t)
   (ii) x(t) = e^-2t u(t)
3. (a) State and prove the following properties of Fourier Transform:
   

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   (i) Time shifting property
   (ii) Frequency shifting property
   (b) Find the Fourier transform of the signal x(t) = e^-at u(t)
   (OR)
4. (a) Obtain the Fourier series representation of the signal x(t) = A cos(ω₀t)
   

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   (b) Find the Fourier transform of the gate function x(t) = A, for |t| < τ and x(t) = 0, for |t| > τ.
5. (a) Define convolution. Explain the properties of convolution.
   (b) Find the convolution of the signals x(t) = e^-2t u(t) and h(t) = u(t)
   (OR)
6. (a) Explain the concept of signal transmission through a linear system.
   

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   (b) Find the impulse response of the systems described by the following differential equations:
   (i) dy(t)/dt + 2y(t) = x(t)
   (ii) d²y(t)/dt² + 5dy(t)/dt + 6y(t) = x(t)
7. (a) Define Laplace transform. Explain the properties of Laplace transform.
   (b) Find the Laplace transform of the signal x(t) = e^-at sin(ωt) u(t)
   

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   (OR)
8. (a) Explain about the region of convergence (ROC) of Laplace transform.
   (b) Find the inverse Laplace transform of the following functions:
   (i) X(s) = 1/(s+1)(s+2)
   (ii) X(s) = s/(s² + 4)

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9. (a) Define Z-transform. Explain the properties of Z-transform.
   (b) Find the Z-transform of the signal x(n) = aⁿ u(n)
   (OR)
10. (a) Explain about the region of convergence (ROC) of Z-transform.
    (b) Find the inverse Z-transform of the following function: X(z) = z/(z-1)(z-2)

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