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From: "Steven G. Johnson" <stevenj@alum.mit.edu>
Newsgroups: comp.soft-sys.matlab
Subject: Re: FFT and DFT in matlab
Date: Thu, 13 Aug 2009 20:19:56 -0700 (PDT)
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On Aug 12, 11:38 pm, Greg <he...@alumni.brown.edu> wrote:
> Both lead to the well known trapezoidal approximation
>
> http://en.wikipedia.org/wiki/Numerical_integration
>
> which downweights the endpoints by a factor of two.

No, this is not correct.  If you are viewing the DFT as a sampled
approximation for Fourier series coefficients, the endpoints are 0 and
N, not 0 and N-1.  If you weight each of these by 1/2 as per the
trapezoidal rule, due to aliasing you get back exactly the DFT
formula.

Regards,
Steven G. Johnson