i need to find the fourier transform of

i get (by definition)

now

so

im stuck as to where to go from here! judging by our notes the next step should be

but i have no idea why this should be (and not even sure its the right step!)

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- October 5th 2011, 05:50 AMwik_chick88fourier transform of f(x)=e^(-ax^2) sin(bx)
i need to find the fourier transform of

i get (by definition)

now

so

im stuck as to where to go from here! judging by our notes the next step should be

but i have no idea why this should be (and not even sure its the right step!) - October 5th 2011, 06:49 AMgirdavRe: fourier transform of f(x)=e^(-ax^2) sin(bx)
You will be able to conclude if you know the value of . If you fix , differentiate this with respect to , and integrate by parts, you will find a differential equation.

- October 9th 2011, 06:12 AMwik_chick88Re: fourier transform of f(x)=e^(-ax^2) sin(bx)
im not sure what you mean here.why would i differentiate it with respect to b?

- October 9th 2011, 06:22 AMgirdavRe: fourier transform of f(x)=e^(-ax^2) sin(bx)
Fix and put . We have hence .

- October 9th 2011, 06:32 AMwik_chick88Re: fourier transform of f(x)=e^(-ax^2) sin(bx)
im a little rusty on integration by parts, i know its \int u dv = uv - \int v du but i cant figure out what you have specified as u and dv above. also im still unsure as to how this helps me??

- October 9th 2011, 06:39 AMgirdavRe: fourier transform of f(x)=e^(-ax^2) sin(bx)
I took and . Now you can solve the previous differential equation, since you can compute .