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From:  dbd <dbd@ieee.org>
Newsgroups: comp.dsp,comp.soft-sys.matlab
Subject: Re: Normalization for DFT (fft in MATLAB)
Date: Wed, 11 Jul 2007 02:35:25 -0700
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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. Dalrymple
http://dbdimages.com