What is fouriertransform x^2 ?

The answer to fouriertransform x^2 is -2pi\delta^{(2)}(ω)

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fouriertransform x^2

fourier transform

x^{2}

- 2 π δ^{(2)} (ω)

Solution steps

F {x^{2}}

Use Fourier Transform table:

F {t^{n}} = 2 π i^{n} δ^{(n)} (ω)

, assuming

n > 0

F {x^{2}} = 2 π i^{2} δ^{(2)} (ω)

= 2 π i^{2} δ^{(2)} (ω)

Simplify

2 i^{2} π δ^{(2)} (ω) : - 2 π δ^{(2)} (ω)

= - 2 π δ^{(2)} (ω)

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What is fouriertransform x^2 ?
The answer to fouriertransform x^2 is -2pi\delta^{(2)}(ω)