Signals and systems electrical engineering miscellaneous


Signals and systems electrical engineering miscellaneous

  1. If L[f(t)] =
    2(s + 2)
    , then ƒ(0+) and ƒ(∞) are given by
    s² + 2s + 5









  1. View Hint View Answer Discuss in Forum

    2(s + 1)
    =
    2(s + 1)
    = 2
    s + 1
    (s² + 2s + 5)(s² + 1)² + 5(s + 1)² + 4

    This is standard Laplace Transform for the function
    L| exp (– at) cos ωt | =
    (s + a)
    (s + a)² + ω²

    where a = 1, ω = 2
    Hence ƒ(t) = 2e– t cos 2t
    ƒ(0) = ƒ(0+) = 2e– 0 cos 2 × 0 = 2
    ƒ(∞) = 2e– ∞ t = 0

    Correct Option: B

    2(s + 1)
    =
    2(s + 1)
    = 2
    s + 1
    (s² + 2s + 5)(s² + 1)² + 5(s + 1)² + 4

    This is standard Laplace Transform for the function
    L| exp (– at) cos ωt | =
    (s + a)
    (s + a)² + ω²

    where a = 1, ω = 2
    Hence ƒ(t) = 2e– t cos 2t
    ƒ(0) = ƒ(0+) = 2e– 0 cos 2 × 0 = 2
    ƒ(∞) = 2e– ∞ t = 0


  1. The unit impulse response of a linear time invariant system is unit step function u(t). For t > 0, the response of the system to an excitation e– at u(t), a > 0 will be









  1. View Hint View Answer Discuss in Forum

    Given: h(t) = u(t)
    x(t) = e–at u(t)

    ∴ Y(s) = X(s) H(s) =
    1
    .
    1
    =
    1
    1
    -
    1
    (s + a)sass + a

    y(t) = 1/a (1 – e– at) u(t)

    Correct Option: B

    Given: h(t) = u(t)
    x(t) = e–at u(t)

    ∴ Y(s) = X(s) H(s) =
    1
    .
    1
    =
    1
    1
    -
    1
    (s + a)sass + a

    y(t) = 1/a (1 – e– at) u(t)



  1. Given the transform pair

    Determine the laplace transform Y(s) of the given time signal in question and choose correct option. y(t) = x(t – 2)









  1. View Hint View Answer Discuss in Forum

    Correct Option: A