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What is the Fourier transform G(ω) of the signal of ?

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  1. 2πeωu(-ω)
  2. πeωu(-ω)
  3. 0.5πeωu(-ω)
  4. 3πeωu(-ω)

Answer (Detailed Solution Below)

Option 1 : 2πeωu(-ω)
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Detailed Solution

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Concept:

As per the property of duality

For, x(t)  x(ω)

x(t)  2πx (-ω)

Calculation: 

For the given question g(t) = 

we know e-at u(t)  

then by property of duality  2πeaω u(-ω)

∴ for a = 1 =  2πeωu(-ω)

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