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Subject: Re: fft amplitude relationship
Date: Tue, 6 Jan 2009 00:07:01 +0000 (UTC)
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"Darren " <dgoshi@ucla.edu> wrote in message <gju67h$avn$1@fred.mathworks.com>...
> Can someone point me to a technical reference/document that explains or discusses this fft (time/freq) amplitude scaling concept. Thanks,
> 
> Darren
> 
> 
> "Ken Garrard" <ken_garrardAT@ncsuDOT.edu> wrote in message <g1jvv5$pq4$1@fred.mathworks.com>...
> > "Bruce " <italianasa84@gmail.com> wrote in message 
> > <g1juri$c4v$1@fred.mathworks.com>...
> > > Thanks, what you mentioned was what I was looking for.
> > > - Bruce
> > 
> > Bruce,
> > 
> > Walter's answer is incomplete.  The DC and Nyquist values 
> > are unique and therefore do not have a 2 in the scale 
> > factor.
> > 
> > time(DC)      = frequency(DC) / N
> > time(Nyquist) = frequency(Nyquist) / N
> > time(all other points) = frequency(all other points) * 2 / N
> > 
> > Note that there is no Nyquist value for odd N.
> > 
> > Ken
> > 

The FFT is essentially an integral operator over a function (usually f(t) but not always).  In the real discrete computer world, integrals are represented by summations.  If you work this through from the basics, then it will become more clear what the scaling relations are.