Re: fourier,units

*To*: mathgroup at smc.vnet.net*Subject*: [mg4004] Re: fourier,units*From*: Harald Berndt <haraldb at nature.berkeley.edu>*Date*: Tue, 14 May 1996 02:38:57 -0400*Organization*: University of California Forest Prodcts Lab*Sender*: owner-wri-mathgroup at wolfram.com

Dorothee Rebscher wrote: > > Hi, > I'm analysing some data with Mathematica using > > Abs[Fourier[data]] > > now my question: > > what kind of units on the axis do I get when my > data are of the form [V] ? > > Thanks in advance, > Dorothee > > email: rebscher at geo.uni-bonn.de Dorothee: The Fourier transform is a linear map. Since your units are no different from scalar multipliers, the output of the map will be multiplied by the same units (V, in your case). A little caution is necessary in interpreting the magnitude values of the FT. The interpretation depends on the definition of the FT (it's in the book). In order to obtain the amplitudes of the Fourier series that will reconstruct your sampled signal (i.e. a1 cos w + b1 sin w + a2 cos 2 w + b2 sin 2 w ....) from the the output of Mma's Fourier[l], you need to scale the output by 1/Sqrt[ Length[l] ]. There's a very nice package called NicerFourier, by Jerry Keiper, Theo Gray and Jerry Glynn, published in "Exploring mathematics with Mathematica." Tschuess, -- ______________________________________________________________________ Harald Berndt, University of California Research Specialist Forest Products Laboratory Phone: 510-215-4224 FAX: 510-215-4299 ______________________________________________________________________ ==== [MESSAGE SEPARATOR] ====