Tue Jan 4 04:55:22 EST 2011
Tim Stilson PhD Introduction
Looks like he finished his PhD in 2006.
His work is mostly not about oversampling and non-linearities, but
about non-oversampled techniques. ( Though I doubt BLIT and BLEP can
be considered non-oversampled, as they are essentially oversampled
Anyways, in the section about discretization of continuous filters he
mentions the Delta Operator on page 33, which also appeared in the
book "Finite Difference Equations" I read the first part of
recently. The idea is to use an integrator/differentiator analogy to
note discrete systems instead of the unit delay as this is more
elegant and more closely resembles the analog case. This then gives
the difference calculus, a set of rules to manipulate formulas with
deltas, as exposed in .
The advantage of this encoding is that it isn't plagued by numerical
issues for highly oversampled systems, i.e. Sigma-Delta modulators.
There should also be a link to automatic differentiation somewhere...
I.e. using memoized / butterfly-style networks instead of
multiplied-out direct formula resembling "convoluted" bell/binomial
shaped coefficients as Tim mentions.
I need to explore other references too.. Goldmine.
Dana Massie: EQ, Harvey Thornburg: NL moog. Antti Huovilainen: moog