Hi Marco On 11-Nov-13 11:26, Marco Lo Monaco wrote:
I basically demonstrate what I already said in my previous posts. The standard state-space approach leads to identical results to your algorithm, I would say even without the trick of the TPT, because of course we are talking about an instantaneous _linear_ feedback.
Of course they are all equivalent, except for some small detail, as e.g. the usage of canonical integrators (although maybe even that was known for long time for trapezoidal integration).
Of course the main purpose of my analysis was to keep in mind that you will _always_ have to deal with an "implicit"/hidden inversion of a matrix A of the analog system (actually (I-A*h/2))
With the filters used in practice, the matrices typically turn out to be either simple or have quite regular structures. This often is given for granted in the 0df (TPT) approach, as you are just solving one linear feedback equation, instead of trying to invert a 5x5 matrix etc. Of course, it's mathematically equivalent, but is much simpler. Also, the division (the most expensive operation) which you have to perform while solving that equation is more or less the same division by a0 which you need to perform in the computation of the BLT-based discrete-time coefficients. So, computationally I think the 0df approach is comparable (even if slighly more expensive at times) to the transfer-function based DF filters, expecially at audio-rate modulations.
Regards, Vadim -- Vadim Zavalishin Reaktor Application Architect Native Instruments GmbH +49-30-611035-0 www.native-instruments.com -- 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