Let f(t) be a continuous-time signal and let F(ω) be its Fourier Transform defined by F (\omega ) = \int ↙\stackrel{\infty}{−\infty}⁡f (t) e^{−j\omega t}dt Define g(t) by g (t) = \int ↙\stackrel{\infty}{−\infty}⁡F (u) e^{−jut}du What is the relationship between f(t) and g(t)?

Correct Answer is : g(t) would be proportional to f(t) if f(t) is an even function

g(t) would always be proportional to f(t)

g(t) would be proportional to f(t) if f(t) is an even function

g(t) would be proportional to f(t) only if f(t) is a sinusoidal function

g(t) would never be proportional to f(t)

GATE Electrical Engineering (EE) 2014 Shift 1 Solved Paper

Question : 45 of 65

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Let f(t) be a continuous-time signal and let F(ω) be its Fourier Transform defined by

F (ω ) = ∫ ↙{−∞}↖{∞}⁡f (t) e^{−jω t}dt

Define g(t) by

g (t) = ∫ ↙{−∞}↖{∞}⁡F (u) e^{−jut}du

What is the relationship between f(t) and g(t)?

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