Am Freitag, den 08.11.2013, 11:03 +0100 schrieb Marco Lo Monaco: > Being in the linear modeling field, I would rather have analized the filter > in the classic virtual analog way, reaching an s-domain transfer function > which has the main advantage that is ready to many discretization > techniques: bilinear (trapezoidal), euler back/fwd, but also multi step like > AdamsMoulton etc. Once you have the s-domain TF you just need to push in s > the correct formula involving z and simplify the new H(z) which is read to > be implemented in DF1/2.
I think a crucial point is that besides replicating steady state response of your analog system, you also want to preserve the time-varying behavior (modulating cutoff frequency) in digital domain. To achieve the latter, your digital system must use a state space representation equivalent to the original circuit, or, how Vadim puts it, "preserve the topology". By starting from an s-TF, however, all this information is lost. This is in particular visible from the fact that implementing different direct forms yields different modulation behavior. BTW, in case you all aren't aware: a work probably relevant to this discussion is the thesis of David Yeh found here: https://ccrma.stanford.edu/~dtyeh/papers/pubs.html When digging through it, in particular the so-called "DK method", you will find many familiar concepts incorporated in a more systematic and general way of discretizing circuits, including nonlinear ones. Can't say how novel all this really is, still it's an interesting read anyway. Dominique -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
