Re: [music-dsp] R: Sallen Key with sin only coefficient computation
On 12/24/14 4:32 AM, Nigel Redmon wrote: Naw, mhos is a one-off. It's fun, pronounceable, and in common use (since 1883!). Don't get carried away. Besides, it makes me think of The Three Stooges, and smile. Siemens makes me think of...er, um—oh Q: so what's long and hard and full of Siemen? yeah—a German multinational corporation headquartered in Berlin and Munich. ;-) -- r b-j r...@audioimagination.com "Imagination is more important than knowledge." A: a submarine. -- 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
Re: [music-dsp] R: Sallen Key with sin only coefficient computation
On 24/12/2014, Nigel Redmon wrote: > Naw, mhos is a one-off. It's fun, pronounceable, and in common use (since > 1883!). Don't get carried away. Besides, it makes me think of The Three > Stooges, and smile. Which in turn makes me wonder what would be measured in curlhis or lharris? -- 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
Re: [music-dsp] R: Sallen Key with sin only coefficient computation
Naw, mhos is a one-off. It's fun, pronounceable, and in common use (since 1883!). Don't get carried away. Besides, it makes me think of The Three Stooges, and smile. Siemens makes me think of...er, um—oh yeah—a German multinational corporation headquartered in Berlin and Munich. ;-) Sent from my iPhone > On Dec 24, 2014, at 3:51 PM, Stefan Stenzel > wrote: > > Time to stop this tragedy, let's also measure frequency in dnoces > > >>> On 24 Dec 2014, at 3:40 , Nigel Redmon wrote: >>> >>> On Dec 23, 2014, at 4:45 AM, r...@audioimagination.com wrote: >>> >>> in units of mhos (reciprocal of ohms)? >> >> Tragically, the formal name for the mho is Siemens, in keeping with naming >> units after the principal scientists involved. (Also, it follows from the >> "Siemens mercury unit".) The tragedy is not only in having such a clever and >> descriptive term replaced by a non-descriptive one, but also the problem >> with the trailing "s" on the latter. 10 mhos = 10 Siemens; 1 mho = 1, er, >> Siemens... >> -- >> 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
Re: [music-dsp] R: Sallen Key with sin only coefficient computation
Time to stop this tragedy, let's also measure frequency in dnoces > On 24 Dec 2014, at 3:40 , Nigel Redmon wrote: > >> On Dec 23, 2014, at 4:45 AM, r...@audioimagination.com wrote: >> >> in units of mhos (reciprocal of ohms)? > > Tragically, the formal name for the mho is Siemens, in keeping with naming > units after the principal scientists involved. (Also, it follows from the > "Siemens mercury unit".) The tragedy is not only in having such a clever and > descriptive term replaced by a non-descriptive one, but also the problem with > the trailing "s" on the latter. 10 mhos = 10 Siemens; 1 mho = 1, er, > Siemens... > -- > 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
Re: [music-dsp] R: Sallen Key with sin only coefficient computation
> On Dec 23, 2014, at 4:45 AM, r...@audioimagination.com wrote: > > in units of mhos (reciprocal of ohms)? Tragically, the formal name for the mho is Siemens, in keeping with naming units after the principal scientists involved. (Also, it follows from the "Siemens mercury unit".) The tragedy is not only in having such a clever and descriptive term replaced by a non-descriptive one, but also the problem with the trailing "s" on the latter. 10 mhos = 10 Siemens; 1 mho = 1, er, Siemens... -- 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
Re: [music-dsp] R: Sallen Key with sin only coefficient computation
On Sun, December 21, 2014 16:46� "Marco Lo Monaco" wrote: > Hello Robert, > I did a similar analysis months ago on the SVF topology Andrew posted at > that time. > The implicit (and most logical) convention is to consider the OTAs as output > current generator (as they should, so that a current flows into the cap), � okay, that acronym could use a little bit of definition: http://en.wikipedia.org/wiki/Operational_transconductance_amplifier . we used to just call them "transconductance amplifiers" (or, more fundamentally, a "voltage-controlled current source") back in the olden daze.� the symbol with the two little circles is new to me (we didn't use it in the 70s). so is "g" marked on the OTA is in units of mhos (reciprocal of ohms)?� what is the value of that "g"?� then the voltage gain would be the transconductance (which i am assuming is "g") times the impedance of the load (which is 1/(jwC)).� and the voltage on the top of the cap is offset by the voltage on the bottom. > the unity/k/mo0/m1/m2 gains as having infinite input impedance and zero > output impedance, � i don't think that transconductance amplifiers have zero output impedance.� they ideally have infinite output impedance.� the current delivered is (ideally) independent of the load connected or (ideally) of the voltage necessary to deliver the prescribed current. � > the summing nodes as having infinite input impedence on > each addend input and zero output on the summed voltage node. > By doing this the analog counterpart of Andrews scheme works. � well, at least i can begin to model the circuit. � that said, and this will make Andrew unhappy, unless there are nonlinear components put into this analysis using trapezoidal integration, there is nothing new to be discovered.� if the entire circuit remains as an LTI (with op-amps or "OTAs" operating in linear mode, resistors, capacitors, even an occasional coil), then an H(s) will pop out with order equal to the number of reactive elements (now sometimes the order of the input-output transfer function is less than the number of caps because of pole-zero cancellation built into the design, but if it were modeled using state-variable convention, the internal order will *always* be equal to the number of reactive elements). so then you get your H(s) and substitute for every integrator (which is s^(-1)) the following: � ��� s^(-1) = T/2 (z+1)/(z-1) or, if you prefer unit delays, ��� s^(-1) = T/2 (1 + z^(-1))/(1 - z^(-1)) � that is what you will get for modeling that continuous-time system with a discrete-time model using trapezoidal integration rule for every continuous-time integrator in the system.� and that is also what you will get when applying the bilinear transform, without compensation for frequency warping, to H(s).� they will and they must come out the same.� 2nd-order analog system gets transformed to a 2nd-order digital system. � now not all biquad filter topologies are the same, even if they have the same H(s).� perhaps the topology you end up with using Andrew's analysis will be better than others (like the Direct Forms or the Lattice or Normallized Lattice or the Rader-Gold form or Hal's SVF) for changing (slewing or modulating) coefficients.� perhaps Andrew's topology will have better roundoff noise behavior at the nodes where quantization must be done.� perhaps there will be better decoupling of coefficients from the user knobs (or modulating waveforms) that change them (like in the lattice, there is one coefficient that solely determines the resonant frequency). � but to determine the biquad coefficients from the user parameters is a solved problem.� to change the simple biquad coefficients (Direct Form x) to Lattice or Normalized Ladder is also not a new thing.� if the purpose is to model the non-linear components in the position in the circuit where they actually exist, then i can see something coming out of this.� otherwise it's really nothing new. � r b-j � � -- 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
Re: [music-dsp] R: Sallen Key with sin only coefficient computation
Hi Marco, Thanks for explaining the diagram to Robert, I am so used to seeing and drawing idealised circuit diagrams like this that I forget people in the DSP aren't as comfortable with them as me. Another feature I forgot to mention, this form is quite fun since your input signals can actually be completely different. So for example you can high pass filter one signal, and low pass filter another with the same cutoff and resonance and the filter mixes them for you at the output. So you could use this as a DJ type filter with two songs as the different inputs and have a crossover type mix between them at the output. This isn't such a big deal in the linear case, you could equally use two filters with the same settings and the cpu difference will be minimal, but for the non-linear case things are more interesting (always the way!). You get both signals contributing to core and resonance drive, so it keeps everything wonderfully balanced and sounds brilliant. David Dixon has confirmed on the Synth DIY email list that this is the same method he uses (although I came up with it independently) in his Intellijel Korgasmatron II filter, well worth checking out: http://www.intellijel.com/eurorack-modules/913-2/ . He actually has two of these input summing sallen key filters in his module. Those analog boys are always one step ahead ;) He released his module in Jan 2013. If anyone is interested in having a listen to the non-linear version please let me know and I'll do some audio demos, the low pass version sounds the same as the MS2 filter in The Drop. Andy -- cytomic -- sound music software -- On 22 December 2014 at 05:46, Marco Lo Monaco wrote: > Hello Robert, > I did a similar analysis months ago on the SVF topology Andrew posted at > that time. > The implicit (and most logical) convention is to consider the OTAs as output > current generator (as they should, so that a current flows into the cap), > the unity/k/mo0/m1/m2 gains as having infinite input impedance and zero > output impedance, the summing nodes as having infinite input impedence on > each addend input and zero output on the summed voltage node. > By doing this the analog counterpart of Andrews scheme works. > > Ciao > > Marco > >> -Messaggio originale- >> Da: music-dsp-boun...@music.columbia.edu [mailto:music-dsp- >> boun...@music.columbia.edu] Per conto di robert bristow-johnson >> Inviato: domenica 21 dicembre 2014 20:25 >> A: music-dsp@music.columbia.edu >> Oggetto: Re: [music-dsp] Sallen Key with sin only coefficient computation >> >> On 12/21/14 1:01 PM, Andrew Simper wrote: >> > I've updated the diagram of the filter to be a little prettier in the >> > full pdf, and I've also uploaded it as a jpg here: >> > >> > http://cytomic.com/files/dsp/SkfInputMixing.jpg >> > >> >> i don't see how one analyzes that circuit since c1 and c2 are not > connected to >> any other impedances. there is no way to determine what the two >> capacitors do. it's really a signal flow diagram (like we do with DSP) > but with >> two mysterious elements added. >> >> -- >> >> r b-j r...@audioimagination.com >> >> "Imagination is more important than knowledge." >> >> >> >> -- >> 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
[music-dsp] R: Sallen Key with sin only coefficient computation
Hello Robert, I did a similar analysis months ago on the SVF topology Andrew posted at that time. The implicit (and most logical) convention is to consider the OTAs as output current generator (as they should, so that a current flows into the cap), the unity/k/mo0/m1/m2 gains as having infinite input impedance and zero output impedance, the summing nodes as having infinite input impedence on each addend input and zero output on the summed voltage node. By doing this the analog counterpart of Andrews scheme works. Ciao Marco > -Messaggio originale- > Da: music-dsp-boun...@music.columbia.edu [mailto:music-dsp- > boun...@music.columbia.edu] Per conto di robert bristow-johnson > Inviato: domenica 21 dicembre 2014 20:25 > A: music-dsp@music.columbia.edu > Oggetto: Re: [music-dsp] Sallen Key with sin only coefficient computation > > On 12/21/14 1:01 PM, Andrew Simper wrote: > > I've updated the diagram of the filter to be a little prettier in the > > full pdf, and I've also uploaded it as a jpg here: > > > > http://cytomic.com/files/dsp/SkfInputMixing.jpg > > > > i don't see how one analyzes that circuit since c1 and c2 are not connected to > any other impedances. there is no way to determine what the two > capacitors do. it's really a signal flow diagram (like we do with DSP) but with > two mysterious elements added. > > -- > > r b-j r...@audioimagination.com > > "Imagination is more important than knowledge." > > > > -- > 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
