source file: mills2.txt
Date: Sun, 15 Oct 1995 21:05:13 -0700

Subject: Adaptive FFT

From: MMCK@delphi.com

Brian says,

>Because the discrete Fourier transform is cyclic and imposes an
>infinite  periodicity (both supersonic and subsonic) on your
>spectrum, you must use a limited fixed sampling rate and
>band-limit your input samples to avoid aliasing (that is, to
>avoid the lowest supersonic and the highest subsonic frequency
>bins from bleeding into your audible frequency bins and 
>contaminating them with inharmonic-sounding spurious garbage). 
>But once you fix your samling rate, you've thrown out all
>information between samples.

This assumes an invariant "time slice" analysis, where the
transform is applied repetitively to a fixed number of data
points.  As I pointed out in a previous post, if you first apply
time domain analysis to identify periodic sequences in the data,
and then "slice" the data according to the results of this
analysis, these considerations don't apply.

It is not Fourier analysis that imposes the condition that "you
must use a limited fixed sampling rate".

Using a variable time slice does make it more difficult to use
FFT's, and it does not solve the problem of aperiodic signals and
strange attractors, etc, but it may help some by limiting the
amount of extraneous data brought in by imposing an outside
frequency on the analysis.

Actually, the sampling frequency is another arbitrary frequency
imposed on the signal.  It might be possible to adaptively vary
the sampling frequency as a function of the output of real time
analysis, and thus minimize this effect also.

Marion

Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl
           with SMTP-OpenVMS via TCP/IP; Mon, 16 Oct 1995 06:07 +0100
Received: from  by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
	for <coul@ezh.nl> id VAA01985; Sun, 15 Oct 1995 21:06:48 -0700
Date: Sun, 15 Oct 1995 21:06:48 -0700
Message-Id: <01HWHKU6U6CO9EDN4E@delphi.com>
Errors-To: madole@ella.mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu