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EC 3354 Signals and Systems question paper, April/May 2025

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Question Paper Code : 90983

B.E./B.Tech. DEGREE EXAMINATIONS, APRIL/MAY 2025.

Third Semester

Electronics and Communication Engineering

EC 3354 — SIGNALS AND SYSTEMS

(Common to : Computer and Communication Engineering/Electronics and Telecommunication Engineering/Medical Electronics)

(Regulations 2021)

Time : Three hoursMaximum : 100 marks

Answer ALL questions.

PART A — (10 × 2 = 20 marks)

  1. 1.

    State the conditions for a system to be causal.

  2. 2.

    Determine whether the signal x(t) = sin^2(2 pi t) is periodic or not.

  3. 3.

    Mention the relationship between Fourier transform and Laplace transform.

  4. 4.

    List the properties of Fourier transform.

  5. 5.

    Given the input x(t) = u(t) and h(t) = delta(t - 1). Find the response y(t).

  6. 6.

    State the initial and final value theorem of Laplace transform.

  7. 7.

    Find DTFT of x(n) = delta(n) + delta(n - 1).

  8. 8.

    Summarize the methods of obtaining inverse Z transform.

  9. 9.

    Determine the convolution of the following signals: x[n] = {1, 2, 3}, h[n] = {1, 2}

  10. 10.

    What are recursive and non-recursive systems?

PART B — (5 × 13 = 65 marks)

  1. 11.
    (a)

    Determine whether the system y(n) = 2x(n) + 5x(n - 1) is static, linear, time invariant, casual and stable or not.

  2. Or
  3. (b)

    A discrete time sequence x(n) = {-1, 0.5, 1.5, 1, 2, 3}. Determine each of the following sequences.

    • (i)x(n - 4)(3)
    • (ii)x(n + 3)(3)
    • (iii)x(3n)(3)
    • (iv)x(2n + 3)(4)
  4. 12.
    (a)

    Find the continuous time fourier transform of the signal x(t) = A sin(2 pi fc t) u(t) and plot its amplitude spectrum.

  5. Or
  6. (b)

    Analyze the inverse laplace transform of the function X(s) = 4 / (s^2 + 6s + 8) for ROCs Re(s) < -4 and -2 > Re(s) > -4.

  7. 13.
    (a)

    The differential equation of the system is given as, d^2y(t)/dt^2 + 7 dy(t)/dt + 12y(t) = dx(t)/dt + 2x(t)

    • (i)Find the frequency response H(j Omega) of the system.(6)
    • (ii)Find the output y(t) of the system for the input x(t) = e^(-2t) u(t).(7)
  8. Or
  9. (b)

    The system transfer function is given as, X(s) = s / (s^2 + 5s + 6). The input to the system is x(t) = e^(-t) u(t). Determine the output assuming zero initial conditions.

  10. 14.
    (a)

    Explain the following properties of discrete time fourier transform.

    • (i)Differentiation in frequency domain(5)
    • (ii)Time reversal(4)
    • (iii)Convolution(4)
  11. Or
  12. (b)

    State and prove sampling theorem.

  13. 15.
    (a)

    For a causal LTI system the input x(n) and output y(n) are related through a difference equation y(n) - (1/6) y(n - 1) - (1/6) y(n - 2) = x(n). Determine the frequency response H(e^jw) and impulse response h(n) of the system.

  14. Or
  15. (b)

    Obtain direct form-I and direct form-II realization of the following system y(n) = 0.75 y(n - 1) - 0.125 y(n - 2) + 6x(n) + 7x(n - 1) + x(n - 2)

PART C — (1 × 15 = 15 marks)

  1. 16.
    (a)

    Find the inverse Z Transform of X(z) = (1 + 2z^-1) / (1 - 2z^-1 + z^-2) when

    • (i)x(n) is causal(8)
    • (ii)x(n) anticausal(7)
  2. Or
  3. (b)

    The transfer function of the discrete time causal system is given as H(z) = (1 - 2z^-1) / (1 - 0.5z^-1 - 0.25z^-2)

    • (i)Find the difference equation of the system.(5)
    • (ii)Draw series and parallel realization of the system.(10)

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