# FFT Algorithms Applications

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

1. FFT algorithm is designed to perform complex operations.
a) True
b) False

2. If x1(n) and x2(n) are two real valued sequences of length N, and let x(n) be a complex valued sequence defined as x(n)=x1(n)+jx2(n), 0≤n≤N-1, then what is the value of x1(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

3. If x1(n) and x2(n) are two real valued sequences of length N, and let x(n) be a complex valued sequence defined as x(n)=x1(n)+jx2(n), 0≤ n≤ N-1, then what is the value of x2(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

4. If X(k) is the DFT of x(n) which is defined as x(n)=x1(n)+jx2(n), 0≤ n≤ N-1, then what is the DFT of x1(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. If X(k) is the DFT of x(n) which is defined as x(n)=x1(n)+jx2(n), 0≤ n≤ N-1, then what is the DFT of x1(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)]

6. If g(n) is a real valued sequence of 2N points and x1(n)=g(2n) and x2(n)=g(2n+1), then what is the value of G(k), k=0,1,2…N-1?
a) X1(k)-W2kNX2(k)
b) X1(k)+W2kNX2(k)
c) X1(k)+W2kX2(k)
d) X1(k)-W2kX2(k)

7. If g(n) is a real valued sequence of 2N points and x1(n)=g(2n) and x2(n)=g(2n+1), then what is the value of G(k), k=N,N-1,…2N-1?
a) X1(k)-W2kX2(k)
b) X1(k)+W2kNX2(k)
c) X1(k)+W2kX2(k)
d) X1(k)-W2kNX2(k)

8. Decimation-in frequency FFT algorithm is used to compute H(k).
a) True
b) False

9. How many complex multiplications are need to be performed for each FFT algorithm?
a) (N/2)logN
b) Nlog2N
c) (N/2)log2N
d) None of the mentioned

10. How many complex additions are required to be performed in linear filtering of a sequence using FFT algorithm?
a) (N/2)logN
b) 2Nlog2N
c) (N/2)log2N
d) Nlog2N

11. How many complex multiplication are required per output data point?
a) [(N/2)logN]/L
b) [Nlog22N]/L
c) [(N/2)log2N]/L
d) None of the mentioned