Signal and systems miscellaneous

Signal and systems miscellaneous

Easy Questions
Moderate Questions
Difficult Questions

Signals and Systems

Signal and systems miscellaneous
  1. The two inputs to an analogue multiplier are x(t) and y(t) with Fourier transforms X(f) and Y(f) respectively. The output z(t) will have a transform Z(t) given by—








  1. View Hint View Answer Discuss in Forum

    z(t) = ∫tα x(λ) Y(t – λ)dλ
    i.e., convolution of the two input signal x(t) and y(t).

    Correct Option: D

    z(t) = ∫tα x(λ) Y(t – λ)dλ
    i.e., convolution of the two input signal x(t) and y(t).

  1. In Laplace transform the variable ‘s’ equal (σ + jω). Which of the following represent the true nature of σ?
    1. σ has a damping effect.
    2. σ is responsible for convergence of internal ∫∞0 f(t) e– st dt.
    3. σ has a value less than zero. Select the correct answer using the codes given below—








  1. View Hint View Answer Discuss in Forum

    We know that s = σ + jω where, σ is known as damping coefficient and
    L {f(t)} = ∫∞0 f(t) e– st dt
    can be expressed as
    L {f(t)} = ∫∞0 f(t) e– (σ + jω)t dt
    = ∫∞0 f(t) e– σt e– jωt dt
    Here factor e– σt factor is called convergence factor.
    Hence alternative (B) is the correct answer.

    Correct Option: B

    We know that s = σ + jω where, σ is known as damping coefficient and
    L {f(t)} = ∫∞0 f(t) e– st dt
    can be expressed as
    L {f(t)} = ∫∞0 f(t) e– (σ + jω)t dt
    = ∫∞0 f(t) e– σt e– jωt dt
    Here factor e– σt factor is called convergence factor.
    Hence alternative (B) is the correct answer.

  1. For a high pass RC circuit, when subjected to a unit step input voltage the voltage across the capacitor will be—








  1. View Hint View Answer Discuss in Forum

    Voltage across capacitor

    =
    1
    V0(s)
    Cs
    Vi(s)
    R + 1
    Cs

    where Vi (t) = u(t)

    Vi (s) =
    1
    s

    V0(s)=Vi (s)
    1
    RCs + 1

    V0(s) =
    1
    		·
    1
    sRCs + 1

    By using partial fraction
    V0(s) =
    A
    		+
    B
    sRCs + 1

    V0(s) =
    A
    		+
    B
    sRCs + 1

    V0(s) =
    1
    		–RC
    sRCs +
    1
    RC

    Taking inverse Laplace transform
    V0(t) = 1 – e– t/RC
    Hence alternative (A) is the correct choice.

    Correct Option: A

    Voltage across capacitor

    =
    1
    V0(s)
    Cs
    Vi(s)
    R + 1
    Cs

    where Vi (t) = u(t)

    Vi (s) =
    1
    s

    V0(s)=Vi (s)
    1
    RCs + 1

    V0(s) =
    1
    		·
    1
    sRCs + 1

    By using partial fraction
    V0(s) =
    A
    		+
    B
    sRCs + 1

    V0(s) =
    A
    		+
    B
    sRCs + 1

    V0(s) =
    1
    		–RC
    sRCs +
    1
    RC

    Taking inverse Laplace transform
    V0(t) = 1 – e– t/RC
    Hence alternative (A) is the correct choice.

  1. A band pass signal having the frequency contents in the range of 1 MHz to 2 MHz is to be sampled. The original signal can be reconstructed, if the minimum sampling rate is—








  1. View Hint View Answer Discuss in Forum

    Minimum sampling rate
    fs = 2fm
    = 2 × 2 × 106 samples/sec.
    = 4 × 106 samples/sec.
    Hence alternative (C) is the correct answer.

    Correct Option: C

    Minimum sampling rate
    fs = 2fm
    = 2 × 2 × 106 samples/sec.
    = 4 × 106 samples/sec.
    Hence alternative (C) is the correct answer.

  1. A function f(t) is an even function if for all values of (t)—
    (T is the time-period of the function)








  1. View Hint View Answer Discuss in Forum

    For a function f(t) to be even the required condition is
    f(t) = f(– t)

    Correct Option: A

    For a function f(t) to be even the required condition is
    f(t) = f(– t)