Fourier Transforms MCQ’s

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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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