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From:  NZTideMan <mulgor@gmail.com>
Newsgroups: comp.dsp,comp.soft-sys.matlab
Subject: Re: Normalization for DFT (fft in MATLAB)
Date: Wed, 11 Jul 2007 03:07:16 -0700
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On Jul 11, 9:35 pm, dbd <d...@ieee.org> wrote:
> On Jul 10, 3:21 pm, "A.E lover" <aelove...@gmail.com> wrote:
>
> > Hi all,
>
> > is it correct that to normalize the output of fft such that a unit
> > sinusoid in the time domain corresponds to unit amplitude in the
> > frequency domain, I simply divide the DFT by the length of data.
> > for example data is x(n), I take N point DFT so the normalized output
> > is  abs(fft(x,N))/N.
>
> > Can you please tell me how to prove this?
>
> > Thanks
>
> > AELOVER
>
> As often happens here, your question is underspecified, but that
> hasn't kept people from throwing out answers.
>
> If your 'unit sinusoid in the time domain' is a constant unit
> amplitude
> complex vector rotating at a bin centered frequency, the N-point FFT
> in
> Matlab will produce an output bin with amplitude N.
>
> If your 'unit sinusoid in the time domain' is a unit peak amplitude
> real sinusoid oscillating between positive and negative peaks at a
> bin centered frequency, the N-point FFT in
> Matlab will produce two output bins with amplitude N/2 at what
> can be interpreted as positive and negative frequency positions.
>
> Note that Tim Wescott's vector of 1's is in the complex vector case.
>
> If you are using real input and want to use only non-negative
> frequencies
> from the FFT, you will have to scale the DC bin differently from the
> positive frequency bins.
>
> Good Luck,
>
> Dale B. Dalrymplehttp://dbdimages.com

Normalisation:
When I use a word,' Humpty Dumpty said, in a rather scornful tone,' it
means just what I choose it to mean, neither more nor less.