# 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 S1 and S2 are linear and time invariant, then interchanging their order does not change the system.
ii) If S1 and S2 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) x1[n] = {1, 0, 2} (Laplace transform) y1 [n] = {0, 1,2}
ii) x2[n] = {0,0, 3} (Laplace transform) y2[n] = {0,1,0,2}
iii) x3[n] = {0,0,0,1} (Laplace transform) y3[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 S1 and S2 are two discrete time systems. Consider the following statements:
i) If S1 and S2 are linear, then S is linear
ii) If S1 and S2 are non-linear, then S is non-linear
iii) If S1 and S2 are causal, then S is causal
iv) If S1 and S2 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. S1 and S2 are two DT systems which are connected together to form a new system. Consider the following statements:
i) If S1 and S2 are non-causal, then S is non-causal
ii) If S1 and/or S2 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 = V2 + 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 R1 is the region of convergence of x (n) and R2 is the region of convergence of y(n), then the region of convergence of x (n) convoluted y (n) is ___________
a) R1 + R2
b) R1 – R2
c) R1 ∩ R2
d) R1 ∪ R2

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|≤f1, |H(f1)|H(0)≥0.95 Then f1 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) 5 Star
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