# Fourier Transforms MCQ’s

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

1. Choose the correct synthesis equation.

a) f(t)=12π∫∞−∞F(ω)e−jωtdω

b) f(t)=12π∫∞−∞F(ω)ejωtdω

c) f(t)=12π∫∞0F(ω)e−jωtdω

d) f(t)=12π∫∞0F(ω)ejωtdω

2. Find the fourier transform of an exponential signal f(t) = e^{-at} u(t), a>0.

a) 1a+jω

b) 1a−jω

c) 1−a+jω

d) 1−a−jω

3. Which of the following is the Analysis equation of Fourier Transform?

a) F(ω)=∫∞−∞f(t)ejωtdt

b) F(ω)=∫∞0f(t)e−jωtdt

c) F(ω)=∫∞0f(t)ejωtdt

d) F(ω)=∫∞−∞f(t)e−jωtdt

4. Find the fourier transform of the function f(t) = e^{-a|t|}, a>0.

a) 2aa2−ω2

b) 2aa2+ω2

c) 2aω2−a2

d) aa2+ω2

5. Find the fourier transform of the gate function.

a) 1ωsin(ωτ2)

b) 1ωcos(ωτ2)

c) 2ωsin(ωτ2)

d) 2ωcos(ωτ2)

6. Bandwidth of the gate function is __________

a) τ Hz

b) 1τ Hz

c) 2τ Hz

d) 2τ Hz

7. Gate function is defined as ______________

a) G(t)={10|t|<τ2elsewhere

b) G(t)={10|t|>τ2elsewhere

c) G(t)={10|t|≤τ2elsewhere

d) G(t)={10|t|≥τ2elsewhere

8. Choose the wrong option.

a) G(t) = rect(tτ)

b) G(t) = u(t + τ2) – u(t-τ2)

c) G(ω) = τ sa(wτ2)

d) G(f) = τ sinc(f)

9. Which of the following is not a fourier transform pair?

a) u(t)↔πδ(ω)+1jω

b) sgn(t)↔2jω

c) A↔2πδ(ω2)

d) G(t)↔sa(ωτ2)

10. Find the fourier transform of the unit step function.

a) πδ(ω) + 1ω

b) πδ(ω) + 1jω

c) πδ(ω) – 1jω

d) δ(ω) + 1jω

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