🚀 go-pugleaf

In article <1992Jul24.203717.2527@bert.eecs.uic.edu>  
eddins@bert.eecs.uic.edu (Dr. Steven L. Eddins) writes:
> croteau@ccwf.cc.utexas.edu (Ed Croteau) writes:
> 
> >Does anyone have any information on the "FOUR1.C" routine in the
> >Numerical Recipes in C book? I believe that the routine as printed
> >(and on a source disk) does not properly compute the FFT (try a 
> >simple real SIN wave and examine the imaginary).  Please let me know
> >if I am wrong about this but it seems like the imaginary part is
> >frequency reversed or something similar.
> 
> Perhaps your difficulty is in their definition of the DFT (Discrete
> Fourier Transform).  See equations (12.1.7) and (12.1.9), and note
> that the signs in the complex exponential terms are reversed from the
> engineering norm.  Or maybe I shouldn't say "norm"---it's reversed
> from the definition *I* use.  ;-)

Bingo! The problem is that mathematicians view the Fourier transform as a  
transform pair and "a tranform is a transform is a transform" while us  
engineers have this perverted idea that a physical meaning should be  
attached to the domain representations.

Anyhow, to solve the problem, simply use the inverse FFT whenever you want  
an FFT and vice versa. Unfortunately, Numerical Recipes is not an isolated  
case of this potentially dangerous definition of the FFT--the Extend  
simulation language on the Mac uses the mathematician's definition and (I  
think) MathCAD also is "in error".

--
Mark Kotanchek
Guidance & Control Dept - 363 ASB
Applied Research Lab/Penn State
P.O. Box 30
State College, PA 16804