This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Frequency Analysis of Discrete Time Signals-1”.

1. What is the Fourier series representation of a signal x(n) whose period is N?

a) ∑N+1k=0ckej2πkn/N**b) ∑N−1k=0ckej2πkn/N**

c) ∑Nk=0ckej2πkn/N

d) ∑N−1k=0cke−j2πkn/N

2. What is the expression for Fourier series coefficient c_{k} in terms of the discrete signal x(n)?

a) 1N∑N−1n=0x(n)ej2πkn/N

b) N∑N−1n=0x(n)e−j2πkn/N

c) 1N∑N+1n=0x(n)e−j2πkn/N**d) 1N∑N−1n=0x(n)e−j2πkn/N**

3. Which of the following represents the phase associated with the frequency component of discrete-time Fourier series(DTFS)?**a) e ^{j2πkn/N}**

b) e

^{-j2πkn/N}

c) e

^{j2πknN}

d) none of the mentioned

4. The Fourier series for the signal x(n)=cos√2πn exists.

a) True**b) False**

5. What are the Fourier series coefficients for the signal x(n)=cosπn/3?**a) c _{1}=c_{2}=c_{3}=c_{4}=0,c_{1}=c_{5}=1/2**

b) c

_{0}=c

_{1}=c

_{2}=c

_{3}=c

_{4}=c

_{5}=0

c) c

_{0}=c

_{1}=c

_{2}=c

_{3}=c

_{4}=c

_{5}=1/2

d) none of the mentioned

6. What is the Fourier series representation of a signal x(n) whose period is N?

a) ∑∞k=0|ck|2**b) ∑∞k=−∞|ck|**

c) ∑0k=−∞|ck|2

d) ∑∞k=−∞|ck|2

7. What is the average power of the discrete time periodic signal x(n) with period N?

a) 1N∑Nn=0|x(n)|

b) 1N∑N−1n=0|x(n)|

c) 1N∑Nn=0|x(n)|2**d) 1N∑N−1n=0|x(n)|2**

8. What is the equation for average power of discrete time periodic signal x(n) with period N in terms of Fourier series coefficient c_{k}?

a) ∑N−1k=0|ck|**b) ∑N−1k=0|ck|2**

c) ∑Nk=0|ck|2

d) ∑Nk=0|ck|

9. What is the Fourier transform X(ω) of a finite energy discrete time signal x(n)?**a) ∑∞n=−∞x(n)e−jωn**

b) ∑∞n=0x(n)e−jωn

c) ∑N−1n=0x(n)e−jωn

d) None of the mentioned

10. What is the period of the Fourier transform X(ω) of the signal x(n)?

a) π

b) 1

c) Non-periodic**d) 2π**

11. What is the synthesis equation of the discrete time signal x(n), whose Fourier transform is X(ω)?

a) 2π∫20πX(ω)ejωndω

b) 1π∫2π0X(ω)ejωndω**c) 12π∫2π0X(ω)ejωndω**

d) None of the mentioned

12. What is the value of discrete time signal x(n) at n=0 whose Fourier transform is represented as below?

a) ω_{c}.π

b) -ω_{c}/π**c) ω _{c}/π**

d) none of the mentioned

13. What is the value of discrete time signal x(n) at n≠0 whose Fourier transform is represented as below?**a) ωcπ.sinωc.nωc.n**

b) −ωcπ.sinωc.nωc.n

c) ωc.πsinωc.nωc.n

d) None of the mentioned

14. The oscillatory behavior of the approximation of XN(ω) to the function X(ω) at a point of discontinuity of X(ω) is known as Gibbs phenomenon.**a) True**

b) False

15. What is the energy of a discrete time signal in terms of X(ω)?

a) 2π∫π−π|X(ω)|2dω**b) 12π∫π−π|X(ω)|2dω**

c) 12π∫π0|X(ω)|2dω

d) None of the mentioned

16. Sampling rate conversion by the rational factor I/D is accomplished by what connection of interpolator and decimator?

a) Parallel**b) Cascade**

c) Convolution

d) None of the mentioned

17. Which of the following has to be performed in sampling rate conversion by rational factor?**a) Interpolation**

b) Decimation

c) Either interpolation or decimation

d) None of the mentioned

18. Which of the following operation is performed by the blocks given the figure below?

a) Sampling rate conversion by a factor I

b) Sampling rate conversion by a factor D

c) Sampling rate conversion by a factor D/I**d) Sampling rate conversion by a factor I/D**

19. The N^{th} root of unity W_{N} is given as _____________

a) e^{j2πN}

b) e^{-j2πN}**c) e ^{-j2π/N}**

d) e

^{j2π/N}

20. Which of the following is true regarding the number of computations requires to compute an N-point DFT?**a) N ^{2} complex multiplications and N(N-1) complex additions**

b) N

^{2}complex additions and N(N-1) complex multiplications

c) N

^{2}complex multiplications and N(N+1) complex additions

d) N

^{2}complex additions and N(N+1) complex multiplications

21. Which of the following is true?

a) W∗N=1NWN−1**b) WN−1=1NWN∗**

c) WN−1=WN∗

d) None of the mentioned

22. What is the DFT of the four point sequence x(n)={0,1,2,3}?

a) {6,-2+2j-2,-2-2j}

b) {6,-2-2j,2,-2+2j}**c) {6,-2+2j,-2,-2-2j}**

d) {6,-2-2j,-2,-2+2j}

23. If X(k) is the N point DFT of a sequence whose Fourier series coefficients is given by c_{k}, then which of the following is true?**a) X(k)=Nc _{k}**

b) X(k)=c

_{k}/N

c) X(k)=N/c

_{k}

d) None of the mentioned

14. What is the DFT of the four point sequence x(n)={0,1,2,3}?

a) {6,-2+2j-2,-2-2j}

b) {6,-2-2j,2,-2+2j}

c) {6,-2-2j,-2,-2+2j}**d) {6,-2+2j,-2,-2-2j}**

25. If W_{4}^{100}=W_{x}^{200}, then what is the value of x?

a) 2

b) 4**c) 8**

d) 16