Signal and systems miscellaneous

Signal and systems miscellaneous

Easy Questions
Moderate Questions
Difficult Questions

Signals and Systems

Signal and systems miscellaneous
  1. A waveform that is neither EVEN nor ODD but has half wave symmetry can be expressed in terms of Fourier series expansion as sum of—








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    Half-wave symmetry can be expressed is terms of Fourier series expansion as sum of odd harmonics of both sine and cosine terms.

    Correct Option: B

    Half-wave symmetry can be expressed is terms of Fourier series expansion as sum of odd harmonics of both sine and cosine terms.

  1. The exponential Fourier co-efficient of a function f(t), whose trigonometric Fourier expansion is found to contain only con sine terms, are—








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    The exponential Fourier coefficients of a function f(t), whose trigonometric Fourier expansion is found to contain only cosine, are always real number.

    Correct Option: B

    The exponential Fourier coefficients of a function f(t), whose trigonometric Fourier expansion is found to contain only cosine, are always real number.

  1. If a plot of a signal x(t) is as shown in the figure—

    Then the plot of the signal x(1 – t) will be—








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    The given figure is

    In order to draw the plot x(1 – t) from the given graph x(t). First apply the shifting operation then reflection, if x(t) is shifted to the left by 1, we get

    Now apply the time reflection property to get
    x(– t + 1) or x(1 – t)

    Hence, alternative (A) is the correct choice.

    Correct Option: A

    The given figure is

    In order to draw the plot x(1 – t) from the given graph x(t). First apply the shifting operation then reflection, if x(t) is shifted to the left by 1, we get

    Now apply the time reflection property to get
    x(– t + 1) or x(1 – t)

    Hence, alternative (A) is the correct choice.

  1. Match List-I with List-II and select the correct answer using the codes given below the Lists—










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    We know that
    (A) f(t) = – f(t) → Odd function wave symmetry.
    (B)

    ∞
    ∑Cnejnω nt → Exponential form of Fourier series
    n = – ∞

    (C) ∫∞– ∞ f(t )e– jωt dt → Fourier transform
    (D) ∫t0 f 1(τ) f 2(t – τ )dτ → Convolution integral
    Hence, alternative (A) is the correct choice.

    Correct Option: A

    We know that
    (A) f(t) = – f(t) → Odd function wave symmetry.
    (B)

    ∞
    ∑Cnejnω nt → Exponential form of Fourier series
    n = – ∞

    (C) ∫∞– ∞ f(t )e– jωt dt → Fourier transform
    (D) ∫t0 f 1(τ) f 2(t – τ )dτ → Convolution integral
    Hence, alternative (A) is the correct choice.

  1. The output of a linear system to a unit step u(t) is t2 e– 2t The system function H(s) is—








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    We know that

    L{tn} →
    Ln
    sn + 1

    At n = 2 L{t2} →
    Ln
    		=
    2·1
    s2 + 1s3

    and L{e– 2t t 2} →
    2
    (s + 2)3

    By applying shifting property.
    Hence, alternative (C) is the correct answer.

    Correct Option: C

    We know that

    L{tn} →
    Ln
    sn + 1

    At n = 2 L{t2} →
    Ln
    		=
    2·1
    s2 + 1s3

    and L{e– 2t t 2} →
    2
    (s + 2)3

    By applying shifting property.
    Hence, alternative (C) is the correct answer.