# DFT Algorithm Computation 2 MCQ’s

This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “DFT Algorithm Computation 2″.

1. For a decimation-in-time FFT algorithm, which of the following is true?

a) Both input and output are in order

b) Both input and output are shuffled

c) Input is shuffled and output is in order

d) Input is in order and output is shuffled

2. If X(k) is the N/2 point DFT of the sequence x(n), then what is the value of X(k+N/2)?

a) F_{1}(k)+F_{2}(k)

b) F_{1}(k)-W_{N}^{k} F_{2}(k)

c) F_{1}(k)+W_{N}^{k} F_{2}(k)

d) None of the mentioned

3. How many complex multiplications are required to compute X(k)?

a) N(N+1)

b) N(N-1)/2

c) N2/2

d) N(N+1)/2

4. For a decimation-in-time FFT algorithm, which of the following is true?

a) Both input and output are in order

b) Both input and output are shuffled

c) Input is shuffled and output is in order

d) Input is in order and output is shuffled

5. If we split the N point data sequence into two N/2 point data sequences f_{1}(n) and f_{2}(n) corresponding to the even numbered and odd numbered samples of x(n), then such an FFT algorithm is known as decimation-in-time algorithm.

a) True

b) False

6. The following butterfly diagram is used in the computation of __________

a) Decimation-in-time FFT

b) Decimation-in-frequency FFT

c) All of the mentioned

d) None of the mentioned

7. If we split the N point data sequence into two N/2 point data sequences f_{1}(n) and f_{2}(n) corresponding to the even numbered and odd numbered samples of x(n) and F_{1}(k) and F_{2}(k) are the N/2 point DFTs of f_{1}(k) and f_{2}(k) respectively, then what is the N/2 point DFT X(k) of x(n)?

a) F_{1}(k)+F_{2}(k)

b) F_{1}(k)-W_{N}^{k} F_{2}(k)

c) F_{1}(k)+W_{N}^{k} F_{2}(k)

d) None of the mentioned

8. The following butterfly diagram is used in the computation of __________

a) Decimation-in-time FFT

b) Decimation-in-frequency FFT

c) All of the mentioned

d) None of the mentioned

9. The total number of complex additions required to compute N point DFT by radix-2 FFT is?

a) (N/2)log_{2}N

b) Nlog_{2}N

c) (N/2)logN

d) None of the mentioned

10. The total number of complex multiplications required to compute N point DFT by radix-2 FFT is?

a) (N/2)log_{2}N

b) Nlog_{2}N

c) (N/2)logN

d) None of the mentioned

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