Properties of Fourier Transforms MCQ’s

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

1. Find the Fourier transform of jπt.
a) sinc(ω)
b) sa(ω)
c) δ(ω)
d) sgn(ω)

2. The Fourier transform of a Gaussian pulse is also a Gaussian pulse.
a) True
b) False

3. The Fourier transform of a function x(t) is X(ω). What will be the Fourier transform of dX(t)dt?
a) X(f)jf
b) j2πfX(f)
c) dX(f)dt
d) jfX(f)

4. Find the Fourier transform of f(t)=te-at u(t).
a) 1(a−jω)2
b) 1(a+jω)2
c) a(a−jω)2
d) ω(a−jω)2

5. Find the Fourier transform of u(-t).
a) πδ(ω) + 1ω
b) πδ(ω) + 1jω
c) πδ(ω) – 1jω
d) δ(ω) + 1jω

6. Find the Fourier transform of 1a+jt.
a) 2πe u(ω)
b) 2πe u(-ω)
c) 2πe-aω u(ω)
d) 2πe-aω u(-ω)

7. Find the Fourier transform of e0t.
a) δ(ω + ω0)
b) 2πδ(ω + ω0)
c) δ(ω – ω0)
d) 2πδ(ω – ω0)

8. Find the Fourier transform of x(t) = f(t – 2) + f(t + 2).
a) 2F(ω)cos⁡2ω
b) F(ω)cos⁡2ω
c) 2F(ω)sin⁡2ω
d) F(ω)sin⁡2ω

9. Find the Fourier transform of e-2t u(t-1).
a) e−2[e−jω12−jω]
b) e2[e−jω12−jω]
c) e−2[ejω12−jω]
d) e−2[e−jω12+jω]

10. If the Fourier transform of g(t) is G(ω), then match the following and choose the right answer.

(i) The Fourier transform of g(t-2) is            (A) G(ω)e^-j2ω
(ii) The Fourier transform of g(t/2) is           (B) G(2ω)  
                                                  (C) 2G(2ω)  
                                                  (D) G(ω-2)

a) (i)-B, (ii)-A
b) (i)-A, (ii)-C
c) (i)-D, (ii)-C
d) (i)-C, (ii)-A

11. Find the Fourier transform of sinc(t).
a) Gπ (ω)
b) G (ω)
c) Gπ2 (ω)
d) Gπ (-ω)

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