This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “FFT Algorithms Applications”.

1. If g(n) is a real valued sequence of 2N points and x_{1}(n)=g(2n) and x_{2}(n)=g(2n+1), then what is the value of G(k), k=N,N-1,…2N-1?

a) X_{1}(k)-W_{2}^{k}X_{2}(k)

b) X_{1}(k)+W_{2}^{k}NX_{2}(k)

c) X_{1}(k)+W_{2}^{k}X_{2}(k)

d) X_{1}(k)-W_{2}^{k}NX_{2}(k)

2. How many complex multiplications are needed to be performed for each FFT algorithm?

a) (N/2)logN

b) Nlog_{2}N

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

d) None of the mentioned

3. If X(k) is the DFT of x(n) which is defined as x(n)=x_{1}(n)+jx_{2}(n), 0≤ n≤ N-1, then what is the DFT of x_{1}(n)?

a) 12[X∗(k)+X∗(N−k)]

b) 12[X∗(k)−X∗(N−k)]

c) 12j[X∗(k)−X∗(N−k)]

d) 12j[X∗(k)+X∗(N−k)]

4. If X(k) is the DFT of x(n) which is defined as x(n)=x_{1}(n)+jx_{2}(n), 0≤ n≤ N-1, then what is the DFT of x_{1}(n)?

a) 12[X∗(k)+X∗(N−k)]

b) 12[X∗(k)−X∗(N−k)]

c) 12j[X∗(k)−X∗(N−k)]

d) 12j[X∗(k)+X∗(N−k)]

5. How many complex additions are required to be performed in linear filtering of a sequence using FFT algorithm?

a) (N/2)logN

b) 2Nlog_{2}N

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

d) Nlog_{2}N

6. If x_{1}(n) and x_{2}(n) are two real valued sequences of length N, and let x(n) be a complex valued sequence defined as x(n)=x_{1}(n)+jx_{2}(n), 0≤n≤N-1, then what is the value of x_{1}(n)?

a) x(n)−x∗(n)2

b) x(n)+x∗(n)2

c) x(n)−x∗(n)2j

d) x(n)+x∗(n)2j

7. If g(n) is a real valued sequence of 2N points and x_{1}(n)=g(2n) and x_{2}(n)=g(2n+1), then what is the value of G(k), k=0,1,2…N-1?

a) X_{1}(k)-W_{2}^{k}NX_{2}(k)

b) X_{1}(k)+W_{2}^{k}NX_{2}(k)

c) X_{1}(k)+W_{2}^{k}X_{2}(k)

d) X_{1}(k)-W_{2}^{k}X_{2}(k)

8. How many complex multiplication are required per output data point?

a) [(N/2)logN]/L

b) [Nlog_{2}2N]/L

c) [(N/2)log_{2}N]/L

d) None of the mentioned

9. FFT algorithm is designed to perform complex operations.

a) True

b) False

10. Decimation-in frequency FFT algorithm is used to compute H(k).

a) True

b) False

11. If x_{1}(n) and x_{2}(n) are two real valued sequences of length N, and let x(n) be a complex valued sequence defined as x(n)=x_{1}(n)+jx_{2}(n), 0≤ n≤ N-1, then what is the value of x_{2}(n)?

a) x(n)−x∗(n)2

b) x(n)+x∗(n)2

c) x(n)+x∗(n)2j

d) x(n)−x∗(n)2j