Re: Fourier Transform

*To*: mathgroup at smc.vnet.net*Subject*: [mg13727] Re: Fourier Transform*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Wed, 19 Aug 1998 01:38:19 -0400*Organization*: University of Western Australia*References*: <6r107l$fih@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Edward Neuman wrote: > Let f(x) = 1/x. If f is regarded as the generalized function, then its > Fourier transform is: > -Pi*I*Sign[t] (see, e.g., G.B. > Folland, "Fourier Analysis and Its Applications," p. 337). > Using Mathematica 3.0 we get: > In[1]:= > << "Calculus`FourierTransform`" > > In[2]:= > FourierTransform[1/x, x, t] > > Out[2]= > 2*I*Pi*(-(1/2) + UnitStep[t, ZeroValue -> 1/2]). > > This agrees with the above result only if t = 0. Bug? No, feature. To handle al the definitions of the FT in the literature, the version 3.0 package has two parameters, FourierFrequencyConstant and FourierOverallConstant. ?FourierFrequencyConstant "FourierFrequencyConstant is an option for FourierTransform and related functions that specifies the constant multiplying I w t in the definition of FourierTransform. The default value of FourierFrequencyConstant is $FourierFrequencyConstant." Cheers, Paul ____________________________________________________________________ Paul Abbott Phone: +61-8-9380-2734 Department of Physics Fax: +61-8-9380-1014 The University of Western Australia Nedlands WA 6907 mailto:paul at physics.uwa.edu.au AUSTRALIA http://www.physics.uwa.edu.au/~paul God IS a weakly left-handed dice player ____________________________________________________________________