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Re: Fourier Transform of a "step" function

• To: mathgroup at smc.vnet.net
• Subject: [mg128514] Re: Fourier Transform of a "step" function
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Thu, 25 Oct 2012 23:36:27 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• Delivered-to: l-mathgroup@wolfram.com
• Delivered-to: mathgroup-newout@smc.vnet.net
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On 10/25/12 at 1:43 AM, etaghtron at gmail.com wrote:

>I have a function, which is defined in this form

>F(x) = a + b x + c x^2(0 < x < x0) F(x) = 0 (x > x0)

>This function is simple. However, its Fourier transform is not
>straightforward due to the limits of the function. I probably can do
>it manually, but I have a few other functions that are more complex
>than this one, which also requires Fourier transform. So I'd like to
>know if Mathematica can handle this.

Rewrite f in terms of HeavisideTheta, i.e.,

f=(a + b x + c x^2)(HeavisideTheta[x]-HeavisideTheta[x-x0])

then

FourierTransform[f,x,w]

will return the desired transform