>I completely agree! I find it mentally easier to think of "energy >stored" in each component rather than "state variables" even though >they are the same. So for musical applications it is important that a >change in the cutoff and resonance doesn't change (until you process >the next sample) the energy stored in each capacitor / inductor / >other energy storage component in your model. Direct form structures >do not have this energy conservation property,
Direct Form I has that property, since the states are simply the previous inputs and outputs (which do not change when the filter coefficients are modulated). It is Direct Form II, and the transposed versions of both Direct Form I and Direct Form II, that exhibit the issue of the states varying with the coefficients. Of course, it's typical when teaching intro DSP to focus on the time-invariant case, and then tell students that Direct Form I is the worst, and Direct Form II Transpose is the best. Which is misleading when you get into the time-variant case! E On Mon, Feb 2, 2015 at 6:39 PM, Andrew Simper <a...@cytomic.com> wrote: > On 2 February 2015 at 18:45, Vadim Zavalishin > <vadim.zavalis...@native-instruments.de> wrote: > >... > > In regards to the artifact minimization, I have only an intuitive > > suggestion. Let's look at the SVF structure in continuous time (e.g. > Fig.5.1 > > on p.77 of > > > http://www.native-instruments.com/fileadmin/ni_media/downloads/pdf/VAFilterDesign_1.0.3.pdf > ) > > and at the structure of the continuous-time integrator (the two untitled > > pictures on p.49 in the same text). It's intuitively clear, that the > > integrator structure, where the cutoff gain precedes the integration > > generates "less" artifacts, since the integrator is "smoothing out" the > > coefficient changes. This leads to the idea that in this case the lowpass > > output of the SVF would be quite reasonable in regards to the artifact > > minimization, since each of the cutoff coefficients is smoothed by an > > integrator and the resonance coefficient is smoothed by both of them. > > Similar considerations can be applied to the other modes, where it's > clear > > that the HP output gets the unsmoothed artifacts from the resonance > changes. > > If we want to build a mixture of LP/BP/HP modes rather than picking the > > outputs one by one, then, maybe it's possible to smooth the artifacts by > > using the transposed (MISO) form of the SVF, but I'm not usre. > >... > > Thanks for your interesting observation of smoothing of cutoff changes > and changes in resonance gain. In this light the MISO form does look > superior, and in my tests has a way more interesting non-linear tone > that a standard SVF, especially the LP, no wonder ARP used this form > in their synths! I have so much to learn still from all the classic > designs. > > > > One would then generally expect other discretization approaches, which do > > not preserve the topology and state variables, such as direct forms to > have > > a way poorer performance in regards to the artifacts, unless, of course, > > it's an approach which specifically targets the artifact minimization in > one > > or the other way. > > > > Regards, > > Vadim > > I completely agree! I find it mentally easier to think of "energy > stored" in each component rather than "state variables" even though > they are the same. So for musical applications it is important that a > change in the cutoff and resonance doesn't change (until you process > the next sample) the energy stored in each capacitor / inductor / > other energy storage component in your model. Direct form structures > do not have this energy conservation property, they are only > equivalent in the LTI case (linear time invariant - ie don't change > your cutoff or resonance ever). Any method that tries to jiggle the > states to preserve the energy would only be trying to do what already > happens automatically with some of state space model, so I feel it is > best to leave such forms for static filtering applications. > > All the best, > > Andy > > > > > > > > On 02-Feb-15 11:18, Ross Bencina wrote: > >> > >> Hello Robert, > >> > >> On 2/02/2015 10:10 AM, robert bristow-johnson wrote: > >>> > >>> also, i might add to the list, the good old-fashioned lattice (or > >>> ladder) filters. > >> > >> > >> In the Laroche paper mentioned earlier [1] he shows that Coupled Form is > >> BIBO stable and Normalized Ladder is stable only if coefficients are > >> varied at most every other sample (which, if adhered to, should also be > >> fine for the current discussion). > >> > >> The Lattice filter is *not* time-varying stable according to Laroche's > >> analysis. I'd be curious to hear alternative views/discussion on that. > >> > >> [1] Laroche, J. (2007) “On the Stability of Time-Varying Recursive > >> Filters,” J. Audio Eng. Soc., vol. 55, no. 6, pp. 460-471, June 2007. > >> > >> Cheers, > >> > >> Ross. > >> -- > >> 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 > > > > > > > > -- > > 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 > -- > 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 > -- 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
