Re: Anthropomorphisms and the inherent periodicity of the DFT

Fred Marshall wrote:
"Stan Pawlukiewicz" <spam@xxxxxxxxxxxxxx> wrote in message news:dq3u8h$nan$1@xxxxxxxxxxxxxxxxxxxxxx

robert bristow-johnson wrote:

(big snip)

s" that the data

passed to it is one period of a discrete, infinite, and periodic
sequence of numbers that has period length of N.

i fail to see this as a misuse of the language to make a point and to
say "The DFT is not a living creature so it cannot make assumptions..."
fails to refute the point i make about the inherent periodic extension
of data made by the DFT.


You really don't make the point either. I've read the periodic extension perspective in Brigham's FFT book, but I have never seen it in in any book that talks about Sturm Louville boundary value problems. There is nothing that makes the periodic extension principle more fundamental than the filter bank perspective,the orthogonal decomposition perspective, or the sampling of the Z transform on the unit circle perspective. It might make circular convolution a bit more intuitive but it really just confuses the hell of people when you present the overlap add method of filtering, and is kind of tangential when you start talking about statistical spectral estimation. 


Stan,

I thought I was following you here but then lost it at the end.

Are for neutral or for .... which convention?

Fred 


in this post tangential= irrelevant.

I don't believe any are wrong, given the context of the signal. If a signal is actually periodic and matched to the sample rate so that the discrete sequence repeats itself, periodical extension of a single period is fine with me. I think the Z transform perspective is the most fundamental for a finite sequence.
.

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