Re: Incorrect Fourier Transorms?
- To: mathgroup at smc.vnet.net
- Subject: [mg24834] Re: Incorrect Fourier Transorms?
- From: "Kevin J. McCann" <Kevin.McCann at jhuapl.edu>
- Date: Tue, 15 Aug 2000 03:04:05 -0400 (EDT)
- Organization: Johns Hopkins University Applied Physics Lab, Laurel, MD, USA
- References: <8n5j1q$n24@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
I get the same results you did, including the correct answers with the default. Looks like a "feature" to me. Kevin <iliketrash at aol.com> wrote in message news:8n5j1q$n24 at smc.vnet.net... > > Hi All: > > In using the symbolic Fourier transform feature of Version 4, > specifically, FourierTransform and InverseFourierTransform, it seems > easy to obtain incorrect results. One would expect the following two > cells to give identical results, but they do not. The first cell > correctly returns the original time function after the two transforms, > but the second cell results in a time-reversed version of the original > time function. The result seems to depend upon when a value is assigned > to the exponential part of the time function. > > The same sort of thing happens when using FourierParameters -> {0, -2 > Pi}. However, using the default values of FourierParameters, or {-1, 1}, > doesn't appear to cause problems. > > Does anyone else have this problem or am I misusing these functions? > > Incidentally, the first cell returns a time function (after double > transformation) that, although correct, is quite far from being fully > simplified; the second cell returns a concise, (although incorrect) > function. > > > > In[121]:= > Clear[b]; > FourierTransform[UnitStep[t]*Exp[-b t], t, w, > FourierParameters -> {1, -1}] > InverseFourierTransform[%, w, t, FourierParameters -> {1, -1}] > b = 2; > Plot[%%, {t, -3, 3}, PlotRange -> All] > > > In[126]:= > a = 2; > FourierTransform[UnitStep[t]*Exp[-a t], t, w, > FourierParameters -> {1, -1}] > InverseFourierTransform[%, w, t, FourierParameters -> {1, -1}] > Plot[%, {t, -3, 3}, PlotRange -> All] > > > > Jerry >