Question

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

(a) \(F(ω) = \int_{-∞}^∞ f(t)e^{jωt} \,dt\)

(b) \(F(ω) = \int_0^∞ f(t)e^{-jωt} \,dt\)

(c) \(F(ω) = \int_0^∞ f(t)e^{jωt} \,dt\)

(d) \(F(ω) = \int_{-∞}^∞ f(t)e^{-jωt} \,dt\)

This question was addressed to me in quiz.

Origin of the question is Fourier Transforms in chapter Fourier Transform of Signals and Systems

Answer 1

Correct option is (d) \(F(ω) = \int_{-∞}^∞ f(t)e^{-jωt} \,dt\)

For explanation I would say: For converting time domain to frequency domain, we use analysis equation. The Analysis equation of Fourier Transform is \(F(ω) = \int_{-∞}^∞ f(t)e^{-jωt} \,dt\).