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*Delivered-to*: mathgroup-newsend@smc.vnet.net

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