# DFT Properties MCQ’s

This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “DFT Properties”.

1. If X(k) is the N-point DFT of a sequence x(n), then circular time shift property is that N-point DFT of x((n-l))_{N} is X(k)e^{-j2πkl/N}.

a) True

b) False

2. If X_{1}(k) and X_{2}(k) are the N-point DFTs of X_{1}(n) and x_{2}(n) respectively, then what is the N-point DFT of x(n)=ax_{1}(n)+bx_{2}(n)?

a) X_{1}(ak)+X_{2}(bk)

b) aX_{1}(k)+bX_{2}(k)

c) e^{ak}X_{1}(k)+e^{bk}X_{2}(k)

d) None of the mentioned

3. If x(n) is real and odd, then what is the IDFT of the given sequence?

a) j1N∑N−1k=0x(k)sin2πknN

b) 1N∑N−1k=0x(k)cos2πknN

c) −j1N∑N−1k=0x(k)sin2πknN

d) None of the mentioned

4. If x(n) and X(k) are an N-point DFT pair, then x(n+N)=x(n).

a) True

b) False

5. If x(n) is real and even, then what is the DFT of x(n)?

a) ∑N−1n=0x(n)sin2πknN

b) ∑N−1n=0x(n)cos2πknN

c) -j∑N−1n=0x(n)sin2πknN

d) None of the mentioned

6. If x(n) and X(k) are an N-point DFT pair, then X(k+N)=?

a) X(-k)

b) -X(k)

c) X(k)

d) None of the mentioned

7. What is the circular convolution of the sequences X_{1}(n)={2,1,2,1} and x_{2}(n)={1,2,3,4}?

a) {14,14,16,16}

b) {16,16,14,14}

c) {2,3,6,4}

d) {14,16,14,16}

8. If X(k) is the N-point DFT of a sequence x(n), then what is the DFT of x*(n)?

a) X(N-k)

b) X*(k)

c) X*(N-k)

d) None of the mentioned

9. If x(n) is a complex valued sequence given by x(n)=x_{R}(n)+jx_{I}(n), then what is the DFT of xR(n)?

a) ∑Nn=0xR(n)cos2πknN+xI(n)sin2πknN

b) ∑Nn=0xR(n)cos2πknN−xI(n)sin2πknN

c) ∑N−1n=0xR(n)cos2πknN−xI(n)sin2πknN

d) ∑N−1n=0xR(n)cos2πknN+xI(n)sin2πknN

10. If X_{1}(n), x_{2}(n) and x_{3}(m) are three sequences each of length N whose DFTs are given as X_{1}(k), X_{2}(k) and X3(k) respectively and X3(k)=X_{1}(k).X_{2}(k), then what is the expression for x_{3}(m)?

a) ∑N−1n=0x1(n)x2(m+n)

b) ∑N−1n=0x1(n)x2(m−n)

c) ∑N−1n=0x1(n)x2(m−n)N

d) ∑N−1n=0x1(n)x2(m+n)N

11. What is the circular convolution of the sequences X_{1}(n)={2,1,2,1} and x_{2}(n)={1,2,3,4}, find using the DFT and IDFT concepts?

a) {16,16,14,14}

b) {14,16,14,16}

c) {14,14,16,16}

d) None of the mentioned

12. If x(n) is a real sequence and X(k) is its N-point DFT, then which of the following is true?

a) X(N-k)=X(-k)

b) X(N-k)=X*(k)

c) X(-k)=X*(k)

d) All of the mentioned

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