$Fourier transform of e^{- 2 | t - 1 |} is$

\frac{4 e^{- j ω}}{4 + ω^{2}}

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\frac{4 e^{j ω}}{(2 + ω)^{2}}

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\frac{4 e^{- j ω}}{(2 + ω)^{2}}

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\frac{4 e^{j ω}}{4 + ω^{2}}

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Solution

The correct option is A $\frac{4 e^{- j ω}}{4 + ω^{2}}$
We know that

$e^{- a | t |} F . T ⟷ \frac{2 a}{a^{2} + ω^{2}}$

$∴ e^{- 2 | t |} F . T ⟷ \frac{4}{4 + ω^{2}}$

$∴ e^{- 2 | t - 1 |} F . T ⟷ \frac{4 e^{- j ω}}{4 + ω^{2}}$

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Similar questions

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