Re: Fourier Question
- To: mathgroup at smc.vnet.net
- Subject: [mg25653] Re: Fourier Question
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Wed, 18 Oct 2000 02:52:25 -0400 (EDT)
- Organization: Universitaet Leipzig
- References: <8seaq8$6s8@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi, Fourier[] make a discrete Fourier transform of equal sampled data on the interval [0,2Pi). It make a comples to complex transform i.e. with basis functions Exp[i k t] and not Cos[] or Sin[] only. A nice introduction text about discret Fourier transform may be at: http://www.ulib.org/webRoot/Books/Numerical_Recipes/bookcpdf.html chapter 12. Mathematica is clearly much smarter than the NR functions but the text is very clear. Regards Jens xxx at uunet.uu.net wrote: > > Hello. I am reading a few books on Fourier Analysis, and I am stuck on > understanding a few concepts. > I was hoping someone who uses this function in Mathematica could point me in > the right direction. > > To make it simple, suppose I have 4 sample points: > > data = {1, 3, 2, 4} > > Fourier[data, FourierParameters -> {-1, 1}] // Chop > > This returns: > > {2.5, -0.25 - 0.25 \[ImaginaryI], -1., -0.25 + 0.25 \[ImaginaryI]} > > I am not sure how to interpret the results. > The best I understand is: > > results = 2.5 + (-.25-.25 I ) Cos[1 t] -1 Sin [ 1 t] + (-.25 + .25 I Cos > 2 t]... > > As you can tell, I am sure this is not correct. > Could someone point me in the right direction. I am sure I will figure it > out from there once I understand how the results are used. > > I am using FourierParameters -> {-1, 1} because I am mostly doing data > analysis. > Thank you in advance for any insight. Dana.