Question

Find the inverse Fourier transform of f(t)=1.

(a) u(t)

(b) δ(t)

(c) e^-t

(d) \(\frac{1}{jω}\)

I got this question in an interview.

I need to ask this question from Inverse Fourier Transform topic in division Fourier Transform of Signals and Systems

Answer 1

The correct answer is (b) δ(t)

Best explanation: We know that the Fourier transform of f(t) = 1 is F(ω) = 2πδ(ω).

Replacing ω with t

F(t) = 2πδ(t)

As per duality property F(t) ↔ 2πf(-ω), we have

2πδ(t) ↔ 2π(1)

δ(t) ↔ 1

Hence, the inverse Fourier transform of 1 is δ(t).