FFT Algorithms Applications MCQ’s

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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 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)

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

3. 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)]

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. 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

6. 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

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=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)

8. 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

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 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

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