Julius Smith <jos@...> writes: > > > I guess there are multiple definitions of "computable". In the > papers I've read (e.g., on wave digital filters), a delay-free loop > is said not to be computable. Solving the linear set equations for a > solution > gives you a new flow graph - a new filter structure that's computable as > drawn. >
Hi Julius, Thanks for your reply. I've never quite understood the mathematical significance of the different approaches so I really appreciate your thoughts on the topic. I know of the topology rearrangement for avoiding delay-free loops, for example in "Detection, Location, and Removal of Delay-Free Loops in Digital Filter Configurations". However, from what I understand of both Vadim's an Raph's approach is that they are "topology preserving". Specifically the state variables from the equations I posted in my previous mail matches the voltages on the capacitors (trapezoidal integration of current) of a similar analog circuit, 4 1-pole filter in series with a feedback path of gain -k. Additionally Raph's State Space Representation is also the identical "topology", so I don't understand how this approach results in a "new flow graph". Raph's notebook specifically cites your paper. As an additional citation besides Raph and Vadim, there is some discussion of the "topology preserving transform" from WIll Pirkle: http://www.willpirkle.com/Downloads/AN-4VirtualAnalogFilters.2.0.pdf Since I am usually not working on the block-diagram level, but so far have understood things more just as a "set of equations", and perhaps since the integration is implicit, that's what allows you to solve the delay-free loop? I've never exactly understood the mathematical implications here. Thanks very much! > > A related term in the finite-differences world is "implicit" versus "explicit" > finite difference schemes, where implicit means you have to solve some > simultaneous equations and explicit means you can compute forward > each time step using previously computed values (a "causal" recursion). > > So, maybe it's just terminology... > > - Julius > > ------------------------------------------------------------------------------ Start Your Social Network Today - Download eXo Platform Build your Enterprise Intranet with eXo Platform Software Java Based Open Source Intranet - Social, Extensible, Cloud Ready Get Started Now And Turn Your Intranet Into A Collaboration Platform http://p.sf.net/sfu/ExoPlatform _______________________________________________ Faudiostream-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/faudiostream-users
