Sat Feb 27 16:35:30 CET 2010

Memoization and filter banks

For ordinary computations a lot can usually be gained by reusing
intermediate results.  The same is probably also true for IIR and FIR
filters.  I.e. when is it more useful to implement serial tructures vs
parallel ones?

This is about ladder and lattice filters.

So, it would probably be useful to think about all kinds of
refactorings of rational functions, and especially the effect of
transformations on the coefficients.

I.e. what would be _really_ interesting is to do on-line filter
design, i.e. adaptive filtering with based on some optimization

Ok, that's the essential insight: it's not about filters.  It's about
coefficients and how to update them.

I.e. given a certain fixed filter topology, how do the coefficients
influence a certain cost function.  Kalman filters etc..
This brings us pretty close to one of Jaques Carette's papers[1][2].

Another interesting one is this [3].

[1] http://www.cas.mcmaster.ca/~carette/newtongen/
[2] http://www.cas.mcmaster.ca/~carette/newtongen/verif_gen.pdf
[3] http://www.cas.mcmaster.ca/~carette/publications/CaretteEtAl2008_AISC.pdf