Question

Choose the correct synthesis equation.

(a) \(f(t) = \frac{1}{2π} \int_{-∞}^∞ F(ω) e^{-jωt} \,dω\)

(b) \(f(t) = \frac{1}{2π} \int_{-∞}^∞ F(ω) e^{jωt} \,dω\)

(c) \(f(t) = \frac{1}{2π} \int_0^∞ F(ω) e^{-jωt} \,dω\)

(d) \(f(t) = \frac{1}{2π} \int_0^∞ F(ω) e^{jωt} \,dω\)

This question was addressed to me in an interview.

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

Answer 1

Correct choice is (b) \(f(t) = \frac{1}{2π} \int_{-∞}^∞ F(ω) e^{jωt} \,dω\)

The explanation: Synthesis equation converts from frequency domain to time domain. The synthesis equation of fourier transform is \(f(t) = \frac{1}{2π} \int_{-∞}^∞ F(ω) e^{jωt} \,dω\).