Signal and systems miscellaneous

Signal and systems miscellaneous

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Signals and Systems

Signal and systems miscellaneous
  1. Which one of the following system is nonlinear? where y(t) = output; x(t) = input








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    After inspecting all the options given in the question, we conclude that there is constant term in option (D), which makes the system non-linear.

    Correct Option: D

    After inspecting all the options given in the question, we conclude that there is constant term in option (D), which makes the system non-linear.

  1. The impulse response h[n] of a linear time-invariant system is given by
    h[n] = u[n + 3] + u[n – 2] – 2u[n – 7]
    where u[n] is the unit step sequence. The above system is—








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    The given impulse response of a system
    h[n] = u[n + 3] + u[n – 2] – 2u[n – 7]
    The given system equation is non-causal for any value of n, since output depends upon the future input.
    The given system is stable.

    Correct Option: A

    The given impulse response of a system
    h[n] = u[n + 3] + u[n – 2] – 2u[n – 7]
    The given system equation is non-causal for any value of n, since output depends upon the future input.
    The given system is stable.

  1. The z-transform of a system is
    H(z) =
    z
    z – 0·2

    If the ROC is |z| < 0.2, then the impulse response of the system is—








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    Given

    H(z) =
    z
    		, |z| < 0·2
    z – 0·2

    then
    h(n) = – (0·2)n u[– n – 1]
    Since, the given z-transform is left-hand sided.

    Correct Option: D

    Given

    H(z) =
    z
    		, |z| < 0·2
    z – 0·2

    then
    h(n) = – (0·2)n u[– n – 1]
    Since, the given z-transform is left-hand sided.

  1. The Fourier transform of a conjugate symmetric function is always—








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    The Fourier transform of a conjugate symmetric function is always conjugate symmetric.

    Correct Option: D

    The Fourier transform of a conjugate symmetric function is always conjugate symmetric.

  1. A continuous-time system is governed by the equation
    3y3(t) + 2y2(t) + y(t) = x2(t) + x(t)
    {y(t) and x(t) respectively are output and input}. The system is—








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    The given continuous-time system equation
    3y3(t) + 2y2(t) + y(t) = x2(t) + x(t)
    ● is non-linear, since there is square terms in input as well in output.
    ● is non-dynamic since the equation does not represents integro-differential equation form.

    Correct Option: D

    The given continuous-time system equation
    3y3(t) + 2y2(t) + y(t) = x2(t) + x(t)
    ● is non-linear, since there is square terms in input as well in output.
    ● is non-dynamic since the equation does not represents integro-differential equation form.