Re: [music-dsp] Sallen Key with sin only coefficient computation
>> I've seen in many Sallen Key circuits people stick the input signal into >> various points to generate some different responses, but always the high >> pass is only 1 pole. > > i haven't seen that with the SK. for HPF, i've only seen it with the the > R's and C's swapped. like with > http://sim.okawa-denshi.jp/en/OPseikiHikeisan.htm . I'm referring to the MS20 and Steiner Parker filters, and also copies of those (eg Doepfer A106), they don't do a 2 pole high pass, so can't generate a proper notch or peaking response. MS20 v2: You can see here in the first filter they stick the input into the base of the second cap (C2): http://machines.hyperreal.org/manufacturers/Korg/MS-synths/schematics/KLM-307.GIF Steiner Parker: Also here, although this is a partially differential design, they do the same thing, a bandpass is generated by putting the input to the base of the first cap, the high pass into the second cap (middle one) - which gives a correct bandpass response, but again only a 1 pole high pass: http://www.cgs.synth.net/modules/cgs35_syntha_vcf.html . The last cap is a differential input of the first one, so they both join to get filtered by the middle cap non-differentially. Andy -- 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
Re: [music-dsp] Sallen Key with sin only coefficient computation
On 12/21/14 1:12 AM, Andrew Simper wrote: Hi Guys, Something I've had on the backburner for a while, but now I've finished my new product I've had time to finish. I've seen in many Sallen Key circuits people stick the input signal into various points to generate some different responses, but always the high pass is only 1 pole. i haven't seen that with the SK. for HPF, i've only seen it with the the R's and C's swapped. like with http://sim.okawa-denshi.jp/en/OPseikiHikeisan.htm . A while back I came up with a version that can also generate a 2 pole high pass, in fact it can generate all the shapes you can by mixing the outputs of an SVF, including notch and peaking or any other summation. Like I did with the SVF some time ago I've also worked out the coefficients for the SKF using Sin only and put it in state increment form. Thanks again to Teemu for pointing out the sin(w) and sin(2*w) sine / cosine generator form as being very low noise and having high accuracy on a KVR thread on efficient sine generation. Like I did a while back with the SVF I've also calculated the DF1 coefficient to SKF with mix parameters which turn out to be identical to the SVF anyway. https://cytomic.com/files/dsp/SkfLinearTrapezoidalSin.pdf again, replacing any analog integrator (like what a capacitor does to current) with trapezoidal integration is identical to the bilinear transform without compensation for frequency warping. and, even though i did a simple proof of it here a while ago, it's not just my opinion: https://en.wikipedia.org/wiki/Bilinear_transform#Discrete-time_approximation . when you compensate the frequency warping applied to the resonant frequency (that's usually the most important frequency), you will get a tan(w0/2) factor in there (and its squared for s^2) where is the normalized angular resonant frequency (0 < w0 < pi). that tan(w0/2) and its square can be replaced with these trig identities: sin(w0) 1 - cos(w0) tan(w0/2) = - (tan(w0/2))^2 = - 1 + cos(w0) 1 + cos(w0) if desired, the cos(w0) can be replaced with cos(w0) = 1 - 2*(sin(w0/2))^2 sometimes that helps numerically - most notably with single-precision floating point application with musically-tuned filters (that is when the resonant frequencies are most often in the bottom 5 or 6 octaves of our hearing range or w0 << pi). -- 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
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
Re: [music-dsp] Sallen Key with sin only coefficient computation
Thanks for spotting the typo Ross! 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 Andy -- cytomic -- sound music software -- On 21 December 2014 at 20:56, Ross Bencina wrote: > On 21/12/2014 5:12 PM, Andrew Simper wrote: > >> and all the other papers (including the SVF version of the same thing I >> did >> a while back) are always available here: >> >> www.cytomic.com/techincal-papers >> > > Actually: > > http://www.cytomic.com/technical-papers > -- > 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] Sallen Key with sin only coefficient computation
On 21/12/2014 5:12 PM, Andrew Simper wrote: and all the other papers (including the SVF version of the same thing I did a while back) are always available here: www.cytomic.com/techincal-papers Actually: http://www.cytomic.com/technical-papers -- 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
