Re: FourierTransform

*To*: mathgroup at smc.vnet.net*Subject*: [mg96023] Re: FourierTransform*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Sun, 1 Feb 2009 04:43:06 -0500 (EST)*References*: <gm1dks$3nk$1@smc.vnet.net>

Hi, the Fourier transform over the interval x in (-Infinity,Infinity) converges only for quadratic integrable functions, i.e., functions where Integrate[Conjugate[f[x]]*f[x],{x,-Infinity,Infinity}]< Infinity This is not the case for Cosh[x], and so no Fourier transform exist. I always thought that one should learn this, before one start to use a computer algebra. Regards Jens Fabian wrote: > I just got the new version (7.0) of Mathematica and was full of hope > that the function FourierTransform is finally improved. (If you have no > idea what I'm talking about try FourierTransform[Cosh[x],x,t] on > Mathematica 6) It turns out that the developers have added support > for the Human Genome project but did not manage to improve the basic > mathematical functions considerably. For example try: > > FourierTransform[1/Cosh[a x],x,t] > > Any ideas why this is the case? I always thought that an average user > is more into Fourier transformation than into image processing? > > Cheers, > Fabian >