# Fourier Series & Coefficients – 2 MCQ’s

This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Fourier Series & Coefficients – 2″.

1. The Fourier series coefficient for the periodic rectangular pulses of height 2A is ____________

a) 2Ajkπsinπ2k

b) 2Ajkπcosπ2k

c) 2Akπsinπ2k

d) 2Akπcosπ2k

2. The Fourier series coefficient for the periodic signal x(t) = sin^{2}t is _____________

a) –14 δ[k-1] + 12 δ[k] – 14 δ[k+1]

b) –14 δ[k-2] + 12 δ[k] – 14 δ[k+2]

c) –12 δ[k-1] + δ[k] – 12 δ[k+1]

d) –12 δ[k-2] + δ[k] – 12 δ[k+2]

3. The Fourier series coefficient for the signal 10δ(t) is ___________

a) 1

b) Cos (π2 k)

c) sin (π2 k)

d) 2

4. The Fourier series coefficient of time domain signal x (t) is X[k] = jδ[k-1] – jδ[k+1] + δ[k+3] + δ[k-3], the fundamental frequency of the signal is ω=2π. The signal is ___________

a) 2(cos 3πt – sin πt)

b) -2(cos 3πt – sin πt)

c) 2(cos 6πt – sin 2πt)

d) -2(cos 6πt – sin 2πt)

5. The Fourier series coefficient of the signal y(t) = x(t-t_{0}) + x(t+t_{0}) is _____________

a) 2 cos (2πt kt_{0}) X[k]

b) 2 sin (2πt kt_{0}) X[k]

c) 2 cos (2πt kt_{0})

d) 2 sin (2πt kt_{0})

6. The Fourier series coefficient of the signal y(t) = Re{x(t)} is ____________

a) X[k]+X[−k]2

b) X[k]−X[−k]2

c) X[k]+X∗[−k]2

d) X[k]−X∗[−k]2

7. The Fourier series coefficient of time domain signal x (t) is X[k] = (−13)|k|. The fundamental frequency of signal is ω=1. The signal is _____________

a) 45+3sin

b) 54+3sint

c) 54+3cost

d) 45+3sint

8. The Fourier series coefficient of the signal y(t) = Even{x(t)} is ___________

a) X[k]+X[−k]2

b) X[k]−X[−k]2

c) X[k]+X∗[−k]2

d) X[k]−X∗[−k]2

9. The Fourier series coefficient of the signal y(t) = d2x(t)dt2 is _____________

a) (2πkT)2X[k]

b) –(2πkT)2X[k]

c) j(2πkT)2X[k]

d) -j(2πkT)2X[k]

10. The discrete time Fourier coefficients of ∑∞m=−∞δ[n−4m] is ____________

a) –14 for all k

b) 14 for all k

c) –12 for all k

d) 12 for all k

11. V(t) = 5, 0≤t<1;

t, t≥1;

The Laplace transform of V (t) is ___________

a) 5s+e−ss2+4e−ss

b) 5s+e−ss2–4e−ss

c) 5s–e−ss2–4e−ss

d) 5s–e−ss2+4e−ss

12. The Fourier series coefficient of the signal y(t) = x(4t-1) is ______________

a) 8πTX[k]

b) 4πTX[k]

c) e−jk8πTX[k]

d) ejk8πTX[k]

13. The discrete time Fourier coefficient of cos^{2}(π8 n) is ______________

a) π2(δ(k+1] + 2δ[k] + δ[k-1])

b) 14j(δ(k+1] + 2δ[k] + δ[k-1])

c) 14(δ(k+1] + 2δ[k] + δ[k-1])

d) π4(δ(k+1] + 2δ[k] + δ[k-1])

14. W(t) = 2, 0≤t<4;

t^{2}, t≥4;

The Laplace transform of W (t) is ___________

a) 2s–e−4s(2s3–8s2–14s)

b) 2s+e−4s(2s3–8s2–14s)

c) 2s–e−4s(2s3+8s2+14s)

d) 2s+e−4s(2s3+8s2+14s)

15. U(t) = 0, 0≤t<7;

(t-7)^{3}, t≥7;

The Laplace transform of U (t) is ___________

a) 6e−7ss4

b) e−7ss4

c) 6e−7ss3

d) 3e−7ss3

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