Question

Which of the following is not a fourier transform pair?

(a) \(u(t) \leftrightarrow πδ(ω) + \frac{1}{jω}\)

(b) \(sgn(t) \leftrightarrow \frac{2}{jω}\)

(c) \(A \leftrightarrow 2πδ(\frac{ω}{2})\)

(d) \(G(t)\leftrightarrow sa(\frac{ωτ}{2})\)

This question was posed to me by my college director while I was bunking the class.

This key question is from Fourier Transforms in portion Fourier Transform of Signals and Systems

Answer 1

Right option is (d) \(G(t)\leftrightarrow sa(\frac{ωτ}{2})\)

Best explanation: \(G(t)\leftrightarrow sa(\frac{ωτ}{2})\) is not a fourier transform pair.

\(G(t)\leftrightarrow τsa(\frac{ωτ}{2})\)  (or) \(G(t)\leftrightarrow G(t)  τ sinc(τf)\).