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GATE EE 2021 Set 1 — Question 42

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MCQ+2 / -0.67MediumFourier Transform PropertiesFourier Analysis & SamplingSignals & Systems

Signals & Systems → Fourier Analysis & Sampling → Fourier Transform Properties

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Question

Let f(t)f(t) be an even function, i.e. f(−t)=f(t)f(-t) = f(t) for all tt. Let the Fourier transform of f(t)f(t) be defined as F(ω)=∫−∞∞f(t)e−jωtdtF(\omega) = \int_{-\infty}^{\infty} f(t) e^{-j\omega t} dt. SupposedF(ω)dω=−ωF(ω) for all ω, and F(0)=1.\frac{dF(\omega)}{d\omega} = -\omega F(\omega) \text{ for all } \omega, \text{ and } F(0) = 1.Then
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