# DFT Algorithm Computation 1 MCQ’s

**This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “DFT Algorithm Computation 1″.**

1. If the arrangement is of the form in which the first row consists of the first M elements of x(n), the second row consists of the next M elements of x(n), and so on, then which of the following mapping represents the above arrangement?

a) n=l+mL

b) n=Ml+m

c) n=ML+l

d) none of the mentioned

2. Which of the following is true regarding the number of computations required to compute an N-point DFT?

a) N^{2} complex multiplications and N(N-1) complex additions

b) N^{2} complex additions and N(N-1) complex multiplications

c) N^{2} complex multiplications and N(N+1) complex additions

d) N^{2} complex additions and N(N+1) complex multiplications

3. The computation of XR(k) for a complex valued x(n) of N points requires _____________

a) 2N^{2} evaluations of trigonometric functions

b) 4N^{2} real multiplications

c) 4N(N-1) real additions

d) All of the mentioned

4. If we store the signal row wise then the result must be read column wise.

a) True

b) False

5. W_{N}^{k+N/2}=?

a) W_{N}^{k}

b) -W_{N}^{k}

c) W_{N}^{-k}

d) None of the mentioned

6. If N=LM, then what is the value of W_{N}^{mqL}?

a) W_{M}^{mq}

b) W_{L}^{mq}

c) W_{N}^{mq}

d) None of the mentioned

7. Which of the following is true regarding the number of computations required to compute DFT at any one value of ‘k’?

a) 4N-2 real multiplications and 4N real additions

b) 4N real multiplications and 4N-4 real additions

c) 4N-2 real multiplications and 4N+2 real additions

d) 4N real multiplications and 4N-2 real additions

8. If we store the signal row wise and compute the L point DFT at each column, the resulting array must be multiplied by which of the following factors?

a) W_{N}^{lq}

b) W_{N}^{pq}

c) W_{N}^{lq}

d) W_{N}^{pm}

9. What is the real part of the N point DFT XR(k) of a complex valued sequence x(n)?

a) ∑N−1n=0[xR(n)cos2πknN–xI(n)sin2πknN]

b) ∑N−1n=0[xR(n)sin2πknN+xI(n)cos2πknN]

c) ∑N−1n=0[xR(n)cos2πknN+xI(n)sin2πknN]

d) None of the mentioned

10. How many complex additions are performed in computing the N-point DFT of a sequence using divide-and-conquer method if N=LM?

a) N(L+M+2)

b) N(L+M-2)

c) N(L+M-1)

d) N(L+M+1)

11. Divide-and-conquer approach is based on the decomposition of an N-point DFT into successively smaller DFTs. This basic approach leads to FFT algorithms.

a) True

b) False

12. Which is the correct order of the following steps to be done in one of the algorithms of the divide and conquer method?

i) Store the signal column wise

ii) Compute the M-point DFT of each row

iii) Multiply the resulting array by the phase factors W_{N}^{lq}.

iv) Compute the L-point DFT of each column.

v) Read the result array row wise.

a) i-ii-iv-iii-v

b) i-iii-ii-iv-v

c) i-ii-iii-iv-v

d) i-iv-iii-ii-v

13. How many complex multiplications are performed in computing the N-point DFT of a sequence using divide-and-conquer method if N=LM?

a) N(L+M+2)

b) N(L+M-2)

c) N(L+M-1)

d) N(L+M+1)

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