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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
______________________________________________________________________


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