Fourier Series & Coefficients – 2 MCQ’s

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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) = sin2t 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-t0) + x(t+t0) is _____________
a) 2 cos (2πt kt0) X[k]
b) 2 sin (2πt kt0) X[k]
c) 2 cos (2πt kt0)
d) 2 sin (2πt kt0)

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 cos2(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;
   t2,          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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