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Quiz: DSP - Discrete Fourier transform

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Number of Questions: 26

Question: 11 -

What is the circular convolution of the sequences X1(n)={2,1,2,1} and x2(n)={1,2,3,4}, find using the DFT and IDFT concepts?

Options:

  1. {14,14,16,16}

  2. None of the mentioned

  3. {16,16,14,14}

  4. {14,16,14,16}

    5. Answer:

    {14,16,14,16}
    Solution:

    Given X1(n)={2,1,2,1}=>X1(k)=[6,0,2,0]
    Given x2(n)={1,2,3,4}=>X2(k)=[10,-2+j2,-2,-2-j2]
    when we multiply both DFTs we obtain the product
    X(k)=X1(k).X2(k)=[60,0,-4,0]
    By applying the IDFT to the above sequence, we get
    x(n)={14,16,14,16}.

Question: 12 -

If X(k) is the N-point DFT of a sequence x(n), then what is the DFT of x*(n)?

Options:

  1. None of the mentioned

  2. X(N-k)

  3. X*(k)

  4. X*(N-k)

    5. Answer:

    X*(N-k)
    Solution:

    Complex conjugate property of DFT, we have if X(k) is the N-point DFT of a sequence x(n), then what is the DFT of x*(n) is X*(N-k).

Question: 13 -

If X1(k) and X2(k) are the N-point DFTs of X1(n) and x2(n) respectively, then what is the N-point DFT of x(n)=ax1(n)+bx2(n)?

Options:

  1. X1(ak)+X2(bk)

  2. eakX1(k)+ebkX2(k)

  3. aX1(k)+bX2(k)

  4. None of the mentioned

    5. Answer:

    aX1(k)+bX2(k)
    Solution not available.

Question: 14 -

What is the circular convolution of the sequences X1(n)={2,1,2,1} and x2(n)={1,2,3,4}?

Options:

  1. {2,3,6,4}

  2. {14,16,14,16}

  3. {14,14,16,16}

  4. {16,16,14,14}

    5. Answer:

    {14,16,14,16}
    Solution:

    x(m)= ∑N−1n=0 x1(n) x2(m−n)N
    For m=0, x2((-n))4={1,4,3,2}
    For m=1, x2((1-n))4={2,1,4,3}
    For m=2, x2((2-n))4={3,2,1,4}
    For m=3, x2((3-n))4={4,3,2,1}
    Now we get x(m)={14,16,14,16}.

Question: 15 -

The computational procedure for Decimation in frequency algorithm takes

Options:

  1. Log2 N2 stages

  2. Log2 N stages

  3. 2Log2 N stages

  4. None of the above

    5. Answer:

    Log2 N stages
    Solution not available.