## Digital Electronic MCQ Set 1

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

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_{k}is the Fourier series coefficient

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

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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

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

a) True

b) False

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_{0}=√2π, we have f

_{0}=1/√2. Since f

_{0}is not a rational number, the signal is not periodic. Consequently, this signal cannot be expanded in a Fourier series.

5. What are the Fourier series coefficients for the signal x(n)=cosπn/3?

a) c1=c2=c3=c4=0,c1=c5=1/2

b) c0=c1=c2=c3=c4=c5=0

c) c0=c1=c2=c3=c4=c5=1/2

d) None of the mentioned

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

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_{k}is the Fourier series coefficient

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

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

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9. What is the Fourier transform X(ω) of a finite energy discrete time signal x(n)?

d) None of the mentioned

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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

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

d) None of the mentioned

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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

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

d) None of the mentioned

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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

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

d) None of the mentioned

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## Digital Electronic MCQ Set 2

1. If the signal to be analyzed is an analog signal, we would pass it through an anti-aliasing filter with B as the bandwidth of the filtered signal and then the signal is sampled at a rate:

a) Fs ≤ 2B

b) Fs ≤ B

c) Fs ≥ 2B

d) Fs = 2B

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2. What is the highest frequency that is contained in the sampled signal?

a) 2Fs

b) Fs/2

c) Fs

d) None of the mentioned

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3. The finite observation interval for the signal places a limit on the frequency resolution.

a) True

b) False

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4. If {x(n)} is the signal to be analyzed, limiting the duration of the sequence to L samples, in the interval 0≤ n≤ L-1, is equivalent to multiplying {x(n)} by:

a) Kaiser window

b) Hamming window

c) Hanning window

d) Rectangular window

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5. What is the Fourier transform of rectangular window of length L?

d) None of the mentioned

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6. If x(n)=cosω_{0}n and W(ω) is the Fourier transform of the rectangular signal w(n), then what is the Fourier transform of the signal x(n).w(n)?

a) 1/2[W(ω-ω_{0})- W(ω+ω_{0})].

b) 1/2[W(ω-ω_{0})+ W(ω+ω_{0})].

c) [W(ω-ω_{0})+ W(ω+ω_{0})].

d) [W(ω-ω_{0})- W(ω+ω_{0})].

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_{0})+ W(ω+ω

_{0})]

7. The characteristic of windowing the signal called “Leakage” is the power that is leaked out into the entire frequency range.

a) True

b) False

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8. Which of the following is the advantage of Hanning window over rectangular window?

a) More side lobes

b) Less side lobes

c) More width of main lobe

d) None of the mentioned

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9. Which of the following is the disadvantage of Hanning window over rectangular window?

a) More side lobes

b) Less side lobes

c) More width of main lobe

d) None of the mentioned

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10. The condition with less number of samples L should be avoided.

a) True

b) False

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## Digital Electronic MCQ Set 3

1. If x(n)=Ae^{jωn} is the input of an LTI system and h(n) is the response of the system, then what is the output y(n) of the system?

a) H(-ω)x(n)

b) -H(ω)x(n)

c) H(ω)x(n)

d) None of the mentioned

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2. If the system gives an output y(n)=H(ω)x(n) with x(n)= Ae^{jωn}as input signal, then x(n) is said to be Eigen function of the system.

a) True

b) False

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3. What is the output sequence of the system with impulse response h(n)=(1/2)^{n}u(n) when the input of the system is the complex exponential sequence x(n)=Ae^{jnπ/2}?

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4. If the Eigen function of an LTI system is x(n)= Ae^{jnπ} and the impulse response of the system is h(n)=(1/2)^{n}u(n), then what is the Eigen value of the system?

a) 3/2

b) -3/2

c) -2/3

d) 2/3

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5. If h(n) is the real valued impulse response sequence of an LTI system, then what is the imaginary part of Fourier transform of the impulse response?

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6. If h(n) is the real valued impulse response sequence of an LTI system, then what is the phase of H(ω) in terms of H_{R}(ω) and H_{I}(ω)?

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7. What is the magnitude of H(ω) for the three point moving average system whose output is given by y(n)=1/3[x(n+1)+x(n)+x(n-1)]?

a) 1/[3|1-2cosω|].

b) 1/[3|1+2cosω|].

c) |1-2cosω|.

d) |1+2cosω|.

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8. What is the response of the system with impulse response h(n)=(1/2)^{n}u(n) and the input signal x(n)=10-5sinπn/2+20cosπn?

d) None of the mentioned

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9. What is the magnitude of the frequency response of the system described by the difference equation y(n)=ay(n-1)+bx(n), 0<a<1?

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10. If an LTI system is described by the difference equation y(n)=ay(n-1)+bx(n), 0 < a < 1, then what is the parameter ‘b’ so that the maximum value of | H(ω)| is unity?

a) a

b) 1-a

c) 1+a

d) None of the mentioned

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11. If an LTI system is described by the difference equation y(n)=ay(n-1)+bx(n), 0

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12. The output of the Linear time invariant system cannot contain the frequency components that are not contained in the input signal.

a) True

b) False

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13. An LTI system is characterized by its impulse response h(n)=(1/2)^{n}u(n). What is the spectrum of the output signal when the system is excited by the signal x(n)=(1/4)^{n}u(n)?

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14. What is the frequency response of the system described by the system function H(z)=1/(1-0.8z^{-1} )?

d) None of the mentioned

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^{-1})=z/(z-0.8) Clearly, H(z) has a zero at z=0 and a pole at p=0.8. hence the frequency response of the system is given as H(ω)= e

^{jω}/(e

^{jω}-0.8).

## Digital Electronic MCQ Set 4

1. If x(n) is a finite duration sequence of length L, then the discrete Fourier transform X(k) of x(n) is given as:

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2. If X(k) discrete Fourier transform of x(n), then the inverse discrete Fourier transform of X(k) is:

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3. A finite duration sequence of length L is given as x(n) =1 for 0≤n≤L-1=0 otherwise , then what is the N point DFT of this sequence for N=L?

a) X(k) =L for k=0, 1,2….L-1

b) X(k) =L for k=0

=0 for k=1,2….L-1

c) X(k) =L for k=0

=1 for k=1,2….L-1

d) None of the mentioned

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4. The Nth rot of unity W_{N} is given as:

a) e^{j2πN}

b) e ^{-j2πN}

c) e^{-j2π/N}

d) e^{j2π/N}

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^{-j2π/N}

5. 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

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

6. Which of the following is true?

d) None of the mentioned

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7. 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}

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_{N}

^{k+N/2}= -W

_{N}

^{k}The matrix W

_{4}may be expressed as

8. 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

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9. 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}

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

a) 2

b) 4

c) 8

d) 16

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## Digital Electronic MCQ Set 5

1. If we split the N point data sequence into two N/2 point data sequences f_{1}(n) and f_{2}(n) corresponding to the even numbered and odd numbered samples of x(n), then such an FFT algorithm is known as decimation-in-time algorithm.

a) True

b) False

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_{1}(n) and f

_{2}(n) corresponding to the even numbered and odd numbered samples of x(n), respectively, that is f

_{1}(n)=x(2n) f

_{2}(n)=x(2n+1) ,n=0,1,2…N/2-1 Thus f

_{1}(n) and f

_{2}(n) are obtained by decimating x(n) by a factor of 2, and hence the resulting FFT algorithm is called a decimation-in-time algorithm.

2. If we split the N point data sequence into two N/2 point data sequences f_{1}(n) and f_{2}(n) corresponding to the even numbered and odd numbered samples of x(n) and F_{1}(k) and F_{2}(k) are the N/2 point DFTs of f_{1}(k) and f_{2}(k) respectively, then what is the N/2 point DFT X(k) of x(n)?

a) F_{1}(k)+F_{2}(k)

b) F_{1}(k)- W_{N}^{k} F_{2}(k)

c) F_{1}(k)+WNk_{N}^{k} F_{2}(k)

d) None of the mentioned

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_{1}(n)=x(2n) f

_{2}(n)=x(2n+1) ,n=0,1,2…N/2-1

3. If X(k) is the N/2 point DFT of the sequence x(n), then what is the value of X(k+N/2)?

a) F_{1}(k)+F_{2}(k)

b) F_{1}(k)- W_{N}^{k} F_{2}(k)

c) F_{1}(k)+W_{N}^{k} F2(k)

d) None of the mentioned

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_{1}(k)+W

_{N}

^{k}F

_{2}(k) We know that F

_{1}(k) and F

_{2}(k) are periodic, with period N/2, we have F

_{1}(k+N/2)= F

_{1}(k) and F

_{2}(k+N/2)= F

_{2}(k). In addition, the factor W

_{N}

^{k+N/2}= -W

_{N}

^{k}. Thus we get, X(k+N/2)= F

_{1}(k)- W

_{N}

^{k}F

_{2}(k).

4. How many complex multiplications are required to compute X(k)?

a) N(N+1)

b) N(N-1)/2

c) N2/2

d) N(N+1)/2

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_{1}(k) requires (N/2)

^{2}complex multiplications. The same applies to the computation of F

_{2}(k). Furthermore, there are N/2 additional complex multiplications required to compute W

_{N}

^{k}. Hence it requires N(N+1)/2 complex multiplications to compute X(k).

5. The total number of complex multiplications required to compute N point DFT by radix-2 FFT is:

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

b) Nlog_{2}N

c) (N/2)logN

d) None of the mentioned

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^{v}, this decimation can be performed v=log

_{2}N times. Thus the total number of complex multiplications is reduced to (N/2)log

_{2}N.

6. The total number of complex additions required to compute N point DFT by radix-2 FFT is:

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

b) Nlog_{2}N

c) (N/2)logN

d) None of the mentioned

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^{v}, this decimation can be performed v=log

_{2}N times. Thus the total number of complex additions is reduced to Nlog

_{2}N.

7. The following butterfly diagram is used in the computation of:

a) Decimation-in-time FFT

b) Decimation-in-frequency FFT

c) All of the mentioned

d) None of the mentioned

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8. For a decimation-in-time FFT algorithm, which of the following is true?

a) Both input and output are in order

b) Both input and output are shuffled

c) Input is shuffled and output is in order

d) Input is in order and output is shuffled

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9. The following butterfly diagram is used in the computation of:

a) Decimation-in-time FFT

b) Decimation-in-frequency FFT

c) All of the mentioned

d) None of the mentioned

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10. For a decimation-in-time FFT algorithm, which of the following is true?

a) Both input and output are in order

b) Both input and output are shuffled

c) Input is shuffled and output is in order

d) Input is in order and output is shuffled