"zero-delay filters" is an unfortunate term for a filter equation that
is expressed in implicit form.
But the similar 'delay-free' term has been used by Fontana, Borin, De
Poli, Rochesso...etc see
https://ieeexplore.ieee.org/document/861380/
https://ieeexplore.ieee.org/document/4558044/
The so-called "topology-preserving transform" was coined by Vadim
Zavalishin from Native instruments in his manuscrit "THE ART OF VA
FILTER DESIGN"
https://www.native-instruments.com/fileadmin/ni_media/downloads/pdf/VAFilterDesign_1.1.1.pdf
It consists in replacing each integrator in a continuous block-diagram
model by its bilinear approximation, where each integrator uses the
transposed direct form II.
This results in an instantaneous feedback loop that needs to be solved
by iterative Newton or fixed-point methods in the non-linear case.
while the linear case can be pre-solved to avoid the implcit iteration.
But similar issues arise when discretizing *any* ODE using an implicit
numerical scheme.
Finally a detailed study of the time-varying properties of *linear*
second order sections implemented using the SVF topology (compared to
the DF2, TDF2, coupled-form...etc) was published in DAFX14.
http://www.dafx14.fau.de/papers/dafx14_aaron_wishnick_time_varying_filters_for_.pdf
Back to Faust, since the language is not procedural, AFAIK, the only way
to implement a fixed-point is to unroll the iteration loop N times and
represent the equivalent block-diagram in faust. The consequence being
that we cannot exit the iteration loop if we have converged or continue
the loop if we don't.
On Thu, Aug 23, 2018 at 12:54 AM pdowling <hello.pdowl...@gmail.com> wrote:
By the way, I don't know why they are called "zero-delay filters". I
just see second-order digital filters,
they are *not* called 'zero-delay filters'. they are called 'zero-delay
feedback (filters)' - 'zdf filters' - the f stands for feedback, as of course
there is no such thing as a filter with no delay :-)
There's no bell filter,
however, because I don't know what that is.
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