# Discrete Fourier Transform MCQ’s

This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Discrete Fourier Transform”.

1. For two discrete time systems, consider the following statements:

i) If S_{1} and S_{2} are linear and time invariant, then interchanging their order does not change the system.

ii) If S_{1} and S_{2} are linear and time variant, then interchanging their order does not change the system

The correct statement from the above is __________

a) Both i & ii

b) Only i

c) Only ii

d) Neither i, nor ii

2. The following input-output pairs have been observed during the operation of a time invariant system

i) x_{1}[n] = {1, 0, 2} (Laplace transform) y_{1} [n] = {0, 1,2}

ii) x_{2}[n] = {0,0, 3} (Laplace transform) y_{2}[n] = {0,1,0,2}

iii) x_{3}[n] = {0,0,0,1} (Laplace transform) y_{3}[n] = {1,2,1}

The conclusion regarding the linearity of the system is _____________

a) Linear

b) Non-linear

c) One more observation is required

d) Conclusion cannot be drawn from observation

3. Given that S_{1} and S_{2} are two discrete time systems. Consider the following statements:

i) If S_{1} and S_{2} are linear, then S is linear

ii) If S_{1} and S_{2} are non-linear, then S is non-linear

iii) If S_{1} and S_{2} are causal, then S is causal

iv) If S_{1} and S_{2} are time invariant, then S is time invariant

The true statements from the above are ____________

a) i, ii, iii

b) ii, iii, iv

c) I, iii, iv

d) I, ii, iii, iv

4. S_{1} and S_{2} are two DT systems which are connected together to form a new system. Consider the following statements:

i) If S_{1} and S_{2} are non-causal, then S is non-causal

ii) If S_{1} and/or S_{2} are unstable, then S is unstable

The correct statement from the above is ____________

a) Both i and ii

b) Only i

c) Only ii

d) Neither i nor ii

5. The Z transform of δ (n − m) is ___________

a) z^{-n}

b) z^{-m}

c) 1z−n

d) 1z−m

6. The period of the signal x(t) = 10 sin 12 π t + 4 cos18 π t is ____________

a) π4

b) 16

c) 19

d) 13

7. Given a signal x[n] = δ[n] + 0.9 δ [n − 6]. The Discrete Time Fourier Transform for 8 points is __________

a) 1 – 0.9 e−j2π8k6

b) 1 + 0.9 e−j2π8k6

c) 1 + 0.9 ej2π8k6

d) 1 – 0.9 ej2π8k6

8. A 10 V is connected across a load whose V-I characteristics is given by 7I = V^{2} + 2V. The internal resistance of the battery is of magnitude 1Ω. The current delivered by the battery is ____________

a) 6 A

b) 5 A

c) 7 A

d) 8 A

9. Given a series RLC circuit with V = 5V, R = 200 kΩ, C = 10µF. Sampling frequency of the circuit is 10 Hz. The expression and the ROC of the z-transform of the sampled signal are ____________

a) 5zz−e−5′, |z|<e^{-5}

b) 5zz−e−0.05′, |z|<e^{-0.05}

c) 5zz−e−0.05′, |z|>e^{-0.05}

d) 5zz−e−5′, |z|>e^{-5}

10. For the circuit given below, if the frequency of the source is 50 Hz, then a value of to which results in a transient free response is _________________

a) 0

b) 1.78 ms

c) 7.23 ms

d) 9.21 ms

11. If R_{1} is the region of convergence of x (n) and R_{2} is the region of convergence of y(n), then the region of convergence of x (n) convoluted y (n) is ___________

a) R_{1} + R_{2}

b) R_{1} – R_{2}

c) R_{1} ∩ R_{2}

d) R_{1} ∪ R_{2}

12. Given a series RLC circuit with V = 5V, R = 200 kΩ, C = 10µF. Sampling frequency of the circuit is 10 Hz. The samples x (n), where n=0,1,2,…., is ___________

a) 5(1-e^{-0.05n})

b) 5e^{-0.05n}

c) 5(1-e^{-5n})

d) 5e^{-5n}

13. If G(f) represents the Fourier Transform of a signal g (t) which is real and odd symmetric in time, then G (f) is ____________

a) Complex

b) Imaginary

c) Real

d) Real and non- negative

14. The system under consideration is an RC low-pass filter with R = 1 kΩ and C = 1 µF. Let H (f) denotes the frequency response of the RC, low-pass filter. Let f1 be the highest frequency, such that 0≤|f|≤f_{1}, |H(f1)|H(0)≥0.95 Then f_{1} is ___________

a) 327.8

b) 163.9

c) 52.2

d) 104.4

15. The response of the LTI system for d2y(t)dt2+dy(t)dt+5y(t)=dx(t)dt. Given that y(0^{–}) = 2, dx(t)dt (at t=0) = 0, x(t) = u(t) is __________

a) 2e^{-t} cos t u(t)

b) 0.5 e^{-t} sin t u(t)

c) 2e^{-t} cos t u(t) + 0.5 e^{-t} sin t u(t)

d) 0.5 e^{-t} cos t u(t-1) + 2e^{-t} sin t u(t-1)

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