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Quiz: DSP – Basics

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Number of Questions: 25

Question: 1 -

Which of the following is done to convert a continuous time signal into discrete time signal?

Options:

  1. Differentiating

  2. Modulating

  3. Integrating

  4. Sampling

    5. Answer:

    Sampling
    Solution:

    A discrete time signal can be obtained from a continuous time signal by replacing t by nT, where T is the reciprocal of the sampling rate or time interval between the adjacent values. This procedure is known as sampling.

Question: 2 -

Which of the following is the odd component of the signal x(t)=e(jt)?

Options:

  1. sint

  2. j*cost

  3. cost

  4. j*sint

    5. Answer:

    j*sint
    Solution:

    Let x(t)=e(jt)
    Now, xo(t)=(1/2)*(x(t)-x(-t))
    =(1/2)*(e(jt) – e(-jt))
    =(1/2)*(cost+jsint-cost+jsint)
    =(1/2)*(2jsint)
    =j*sint.

Question: 3 -

All energy signals will have an average power of ___________

Options:

  1. Zero

  2. Cannot be calculated

  3. Infinite

  4. Positive

    5. Answer:

    Zero
    Solution:

    For any energy signal, the average power should be equal to 0 i.e., P=0.

Question: 4 -

For a continuous time signal x(t) to be periodic with a period T, then x(t+mT) should be equal to ___________

Options:

  1. x(mt)

  2. x(t)

  3. x(-t)

  4. x(mT)

    5. Answer:

    x(t)
    Solution:

    If a signal x(t) is said to be periodic with period T, then x(t+mT)=x(t) for all t and any integer m.

Question: 5 -

The even part of a signal x(t) is?

Options:

  1. x(t)-x(-t)

  2. (1/2)*(x(t)-x(-t))

  3. x(t)+x(-t)

  4. (1/2)*(x(t)+x(-t))

    5. Answer:

    (1/2)*(x(t)+x(-t))
    Solution:

    Let x(t)=xe(t)+xo(t)
    =>x(-t)=xe(-t)-xo(-t)
    By adding the above two equations, we get
    xe(t)=(1/2)*(x(t)+x(-t)).