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From: dbd <dbd@ieee.org>
Newsgroups: comp.soft-sys.matlab
Subject: Re: FFT and DFT in matlab
Date: Thu, 13 Aug 2009 11:47:32 -0700 (PDT)
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On Aug 12, 8:38 pm, Greg <he...@alumni.brown.edu> wrote:
> ...
>
> http://en.wikipedia.org/wiki/Numerical_integration
>
> which downweights the endpoints by a factor of two.
>
> ...
> Greg

Thank you for providing the reference. I think that a comparison of
the references in this thread show that "numerical integration" and
"harmonic analysis" are significantly different viewpoints on:

> 2. Analysis of discrete signals and systems.

One of the obvious differences is that  "harmonic analysis" deals with
an extent of N sample intervals on the basis of N samples while
"numerical integration" deals with an extent of N-1 sample intervals
on the basis of N samples. This is what seems to require the different
weighting of the end samples.

I have not found any published uniform or nonuniform DFT algorithm
that takes the "numerical integration" viewpoint. Have you? The wiki/
Numerical_Integration article makes no pretense of representing a DFT.
This makes your suggestion to the OP about failure to properly
numerically integrate seem an unlikely source of error between the
OP's implementation and any other DFT or non-uniform DFT algorithm
implementation.

Dale B. Dalrymple