Fourier transform of xt- t-3e-3-t- is

Δ (t)F.T⟷1 3e^ 3|t|F.T⟷3×2× 3ω^2+9=18ω^2+9 x(t)F.T⟷1+18ω^2+9 x(t)F.T⟷ω^2+27ω^2+9 ...

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Byju's Answer

Standard XII

Mathematics

Integration by Parts

Fourier trans...

Question

Fourier transform of $x (t) = δ (t) + 3 e^{- 3 | t |}$ is

$\frac{ω^{2} + 9}{ω^{2} + 27}$

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$\frac{ω^{2} + 27}{ω^{2} - 9}$

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$\frac{ω^{2} + 27}{ω^{2} + 9}$

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$\frac{ω^{2} + 9}{ω^{2} - 9}$

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Solution

The correct option is C
$\frac{ω^{2} + 27}{ω^{2} + 9}$

$δ (t) F . T ⟷ 1$

$3 e^{- 3 | t |} F . T ⟷ 3 \times \frac{2 \times 3}{ω^{2} + 9} = \frac{18}{ω^{2} + 9}$

$x (t) F . T ⟷ 1 + \frac{18}{ω^{2} + 9}$

$x (t) F . T ⟷ \frac{ω^{2} + 27}{ω^{2} + 9}$

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Fourier transform of x(t)=δ(t)+3e−3|t| is

The correct option is C ω2+27ω2+9 δ(t)F.T⟷1 3e−3|t|F.T⟷3×2×3ω2+9=18ω2+9 x(t)F.T⟷1+18ω2+9 x(t)F.T⟷ω2+27ω2+9

Fourier transform of $x (t) = δ (t) + 3 e^{- 3 | t |}$ is

The correct option is C
$\frac{ω^{2} + 27}{ω^{2} + 9}$

$δ (t) F . T ⟷ 1$

$3 e^{- 3 | t |} F . T ⟷ 3 \times \frac{2 \times 3}{ω^{2} + 9} = \frac{18}{ω^{2} + 9}$

$x (t) F . T ⟷ 1 + \frac{18}{ω^{2} + 9}$

$x (t) F . T ⟷ \frac{ω^{2} + 27}{ω^{2} + 9}$