Let f(t) be a continuous-time signal and let F(ω) be its Fourier Transform defined by\(F\left( \omega \right) = \mathop \smallint \limits_{ - \infty }^\infty f\left( t \right){e^{ - j\omega t}}dt\)Define g(t) by\(g\left( t \right) = \mathop \smallint \limits_{ - \infty }^\infty F\left( u \right){e^{ - ju t}}du\)What is the relationship between f(t) and g(t)?

• A. g(t) would always be proportional to f(t)
• B. g(t) would be proportional to f(t) if f(t) is an even function
• C. g(t) would be proportional to f(t) only if f(t) is a sinusoidal function
• D. g(t) would never be proportional to f(t)