[PD] better tabread4~

Charles Henry czhenry at gmail.com
Thu Jul 3 21:34:17 CEST 2008

On Wed, Jul 2, 2008 at 1:51 PM, Matt Barber <brbrofsvl at gmail.com> wrote:
> Seriously though, I tend to agree with you -- this should explain my
> unease about searching for every polynomial possibility with a certain
> number of points.  I want to help out as much as I can, but I just
> don't want to be the one to close a door on an option.  I am only
> qualified to deliver some of the formulae and maybe do some of the
> programming, but I don't pack the mathematical guns to do the kinds of
> analytical work Chuck has been doing.

I have a bit of insight on the math of the problem, because I've been
working through some examples.  And I still don't have an objective
idea how to design the right interpolator for the job.  Because
there's so many possibilities, I think we should employ a few
heuristics to guide the design.  I think we are working with 3 main
types of variations (please suggest more if possible):
1.  degree of polynomial
2.  number of points
3.  setting constraints on derivatives and points

My observations:
1. increasing the degree of polynomial allows to increase the rate of
stop-band falloff (e.g 1/w^3 is best possible for a cubic, 1/w^5 is
best possible for 5th degree)
2. increasing number of points allows improved derivatives, leading to
better high-frequency response

I think we could even turn this around, and specify aspects of the
function, like rate of stop-band falloff and location of -3 dB cutoff
frequency (which it turns out, is much lower than the Nyquist
frequency).  That might be the best case for what we can do.


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