Re: FourierTransform on UnitStep

*To*: mathgroup at smc.vnet.net*Subject*: [mg14473] Re: FourierTransform on UnitStep*From*: John Doty <jpd at w-d.org>*Date*: Fri, 23 Oct 1998 20:58:51 -0400*Organization*: Wampler-Doty Family*References*: <70k58j$eon@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Normand Leclerc wrote: > I am a new EE Student and I'm just begining with Fourier transforms. I > was using Mathematica at school when I saw something I just couldn't > figure out. > > FourierTransform[UnitStep[t],t,w] gives me I/w + pi DiracDelta[w] > > I learned that it should give me pi DiracDelta[w]-I/w or 1/Iw + pi > DiracDelta[w]. > > Am I missing something or is there a bug in the FourierTransform > package? They are using Mathematica 3.0 There are two conventions for the sign of I in Fourier analysis: the "physics" convention, and the "EE" convention. Mathematica uses the "physics" convention. If you set: $FourierFrequencyConstant = -1 you'll get the behavior you want. This clash of conventions often causes serious headaches. I have heard that a certain array processor manufacturer once, in response to a customer complaint, changed their firmware to use the "correct" convention (according to that customer), without changing the documentation or otherwise disseminating news of this change. As a result, geologists interpreting the first synthetic aperture radar maps of Venus from the Magellan mission struggled to find a geological explanation for unexpected small-scale smoothness of the planet (the problem was eventually discovered). Be careful! -- John Doty "You can't confuse me, that's my job." Home: jpd at w-d.org Work: jpd at space.mit.edu