Signal and systems miscellaneous

Signal and systems miscellaneous

Easy Questions
Moderate Questions
Difficult Questions

Signals and Systems

Signal and systems miscellaneous
  1. A function f(t) is an odd function, if for all values of t—








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

    Correct Option: B

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

  1. A sinusoidal waveform is mathematically expressed by—








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    Sinusoidal waveform is given below

    having amplitude A and time period 2π.
    From the waveform, we see that this is symmetric about the origin i.e., an odd function.
    Hence alternative (A) is the correct answer.

    Correct Option: A

    Sinusoidal waveform is given below

    having amplitude A and time period 2π.
    From the waveform, we see that this is symmetric about the origin i.e., an odd function.
    Hence alternative (A) is the correct answer.

  1. The spectral density of a random signal is given by π[δ(ω – ω0) + δ(ω + ω0)]. The auto-correlation function of the signal is—








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    We know that spectral density of is the Fourier transform of autocorrelation function.
    Let the autocorrelation function Rxx.
    (A) Rxx(τ) = cos ω0τ

    Rxx(τ) =
    e– jω0T + e– jω0T
    2

    or Sxx(ω) = ∫∞– ∞ Rxx e– jωτdτ
    or Sxx(ω) = ∫∞– ∞
    e– jω0τ + e– jω0τ
    		e– jωτdτ
    2

    or Sxx(ω) = π[δ(ω – ω0) + δ(ω + ω0)]
    (by using frequency shifting property)
    There, no need to solve other alternative. This is the correct answer.

    Correct Option: A

    We know that spectral density of is the Fourier transform of autocorrelation function.
    Let the autocorrelation function Rxx.
    (A) Rxx(τ) = cos ω0τ

    Rxx(τ) =
    e– jω0T + e– jω0T
    2

    or Sxx(ω) = ∫∞– ∞ Rxx e– jωτdτ
    or Sxx(ω) = ∫∞– ∞
    e– jω0τ + e– jω0τ
    		e– jωτdτ
    2

    or Sxx(ω) = π[δ(ω – ω0) + δ(ω + ω0)]
    (by using frequency shifting property)
    There, no need to solve other alternative. This is the correct answer.

  1. The trigonometric Fourier series expansion of an even function that is also half-wave symmetric shall contain—








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    In the trigonometric Fourier expansion of an even function that is also half-wave symmetric shall contain only odd harmonics of cosine terms.

    Correct Option: A

    In the trigonometric Fourier expansion of an even function that is also half-wave symmetric shall contain only odd harmonics of cosine terms.

  1. A waveform with discontinuities is always characterised by—








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    A waveform with discontinuities is always characterized by strong harmonic content.

    Correct Option: B

    A waveform with discontinuities is always characterized by strong harmonic content.