GATE 2024 BM – Question 22

Signals and Systems · Laplace and Fourier Transforms · 1 mark · Multiple choice

Find the continuous-time Fourier transform of $e^{-|2t|}$, with kernel e⁻ʲωᵗ.

Show answer and explanation

Correct answer: (B) $4/(4+\omega^2)$

Explanation

For e^(−a|t|), split the integral at zero to obtain 1/(a+jω)+1/(a−jω)=2a/(a²+ω²). With a=2 the transform is 4/(4+ω²), B.

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