Common Fourier Transforms MCQ’s

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

1. The trigonometric Fourier series of a periodic time function can have only ___________
a) Only cosine terms
b) Only sine terms
c) Both cosine and sine terms
d) Dc and cosine terms

2. The Fourier transform of the signal δ(t+1) + δ(t-1) is ____________
a) 21+jω
b) 21−jω
c) 2 cos ω
d) 2 sin ω

3. The Fourier series of an odd periodic function, contains __________
a) Only odd harmonics
b) Only even harmonics
c) Only cosine terms
d) Only sine terms

4. The trigonometric Fourier series of an even function of time does not have ___________
a) The dc term
b) The cosine terms
c) The sine terms
d) The odd harmonic terms

5. For a periodic signal () = 30 sin 1000 + 10 cos 3000 + 6 sin(5000 + 4), the fundamental frequency in rad/s is __________
a) 1000
b) 3000
c) 5000
d) 15000

6. Which of the following cannot be the Fourier series expansion of a periodic signal?
a) x1(t) = 2 cos + 3 cos 3
b) x2(t) = 2 cos + 7 cos
c) x3(t) = cos + 0.5
d) x4(t) = 2 cos 1.5 + sin 3.5t

7. The Fourier transform of the signal ∑∞m=0amδ(t−m) is _____________
a) 11+ae−jω
b) 11+aejω
c) 11−aejω
d) 11−ae−jω

8. The Fourier transform of the signal sin(2πt) e-t u (t) is ____________
a) 12j(11+j(ω−2π)+11+j(ω+2π))
b) 12j(11+j(ω−2π)–11+j(ω+2π))
c) 12j(11+j(ω+2π)–11+j(ω−2π))
d) 1j(11+j(ω+2π)–11+j(ω−2π))

9. The Fourier transform of the signal sgn (t) is ____________
a) −2jω
b) 4jω
c) 2jω
d) 1jω+1

10. The Fourier transform of the signal 1a2+w2 is _____________
a) πaea|ω|
b) πae−a|ω|
c) 2ae−a|ω|
d) πaea|ω|

11. The Fourier transform of the signal u(t+1) – 2u(t) + u(t-1) is ____________
a) 2sinω−2jω
b) 2cosω−2jω
c) 2cosω+2jω
d) 2sinω+2jω

12. The Fourier transform of the signal u (t) is ____________
a) π δ(ω)
b) 1jω
c) π δ(ω) + 1jω
d) –1jω

13. The Fourier transform of the signal e-|t| in [-2,2] is _____________
a) 2+2e−2cos2ω+2ωe−2sin2ω1−ω2
b) 2–2e−2cos2ω–2ωe−2sin2ω1+ω2
c) 2–2e−2cos2ω+2ωe−2sin2ω1+ω2
d) 2+2e−2cos2ω+2ωe−2sin2ω1−ω2

14. The Inverse Fourier transform of the signal 2πδ(ω) + πδ(ω-4π) + πδ(ω+4π) is ______________
a) 2π(1 – cos 4πt)
b) π (1 – cos 4πt)
c) 1 + cos 4πt
d) 2 π (1 + cos 4πt)

15. Given x (t) = 1, |t|<T1; 0, T1<|t|<T02. The DC component of x(t) is ___________
a) T1T0
b) 2T1T0
c) T12T0
d) T0T1

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