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Date: Tue, 10 Jul 2007 15:40:15 -0700
From: Tim Wescott <tim@seemywebsite.com>
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Subject: Re: Normalization for DFT (fft in MATLAB)
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A.E lover 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
> 
Not in general.  It seems like everyone and his brother has a different 
way of normalizing the FFT and IFFT internally -- you need to check to 
see what your software package does and go with the flow.

Do an FFT on a vector of ones.  Your result should be non-zero for the 
first bin, and darn close to zero everywhere else.  Use the value of the 
non-zero bin to scale your results.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" gives you just what it says.
See details at http://www.wescottdesign.com/actfes/actfes.html