� hmmmm. �i wonder if someone is trying to tell me something.... � ---------------------------- Original Message ---------------------------- Subject: confirm a2ab2276c83b0f9c59752d823250447ab4b666 From: music-dsp-requ...@music.columbia.edu Date: Mon, March 28, 2016 2:31 pm To: r...@audioimagination.com -------------------------------------------------------------------------- > Mailing list removal confirmation notice for mailing list music-dsp > > We have received a request for the removal of your email address, > "r...@audioimagination.com" from the music-dsp@music.columbia.edu > mailing list. To confirm that you want to be removed from this > mailing list, simply reply to this message, keeping the Subject: > header intact. Or visit this web page: > > https://lists.columbia.edu/mailman/confirm/music-dsp/a2ab2276c83b0f9c59752d823250447ab4b666 > > > Or include the following line -- and only the following line -- in a > message to music-dsp-requ...@music.columbia.edu: > > confirm a2ab2276c83b0f9c59752d823250447ab4b666 > > Note that simply sending a `reply' to this message should work from > most mail readers, since that usually leaves the Subject: line in the > right form (additional "Re:" text in the Subject: is okay). > > If you do not wish to be removed from this list, please simply > disregard this message. If you think you are being maliciously > removed from the list, or have any other questions, send them to > music-dsp-ow...@music.columbia.edu. > > i think *someone* is being a wee bit malicious. �or at least a bit mischievous. (BTW, i changed the number enough that i doubt it will work for anyone. �but try it, if you want.) � � ---------------------------- Original Message ---------------------------- Subject: Re: [music-dsp] Changing Biquad filter coefficients on-the-fly, how to handle filter state? From: "vadim.zavalishin" <vadim.zavalis...@native-instruments.de> Date: Mon, March 28, 2016 2:20 pm To: r...@audioimagination.com music-dsp@music.columbia.edu -------------------------------------------------------------------------- > robert bristow-johnson писал 2016-03-28 17:57: >> using the trapezoid rule to model/approximate the integrator of an >> analog filter is no different than applying bilinear transform >> (without compensation for frequency warping) to the same integrator. >> >> s^(-1) <--- T/2 * (1 + z^(-1)) / (1 - z^(-1)) > > This statement implies the LTI case, where the concept of the transfer > function exists. i didn't say that. �i said "applying ... to the same integrator." �about each individual "transfer function" that looks like "s^(-1)" � > In the topic of this thread we are talking about > time-varying case, this means that the transfer function concept doesn't > apply anymore. � well, there's slow time and there's fast time. �and the space between the two depends on how wildly one twists the knob. �while the filter properties are varying, we want the thing to sound like a filter (with properties that vary). �there *is* a concept of frequency response (which may vary). � for each individual integrator you are replacing the continuous-time-domain equivalent of s^(-1) with the discrete-time-domain equivalent of T/2 * (1 + z^(-1)) / (1 - z^(-1)), which is the same as the trapezoid rule. � > Specifically, filters with identical *formal* transfer > functions will behave differently and this is exactly the topic of the > discussion. i didn't say anything about a "transfer function", until this post. �i am saying that the trapezoidal rule for modeling integrators is replacing those integrators (which by themselves are LTI and *do* happen to have a transfer function of "s^(-1)") with whatever "T/2 * (1 + z^(-1)) / (1 - z^(-1))"� means. �and that's the same as the trapezoid rule. �(the stuff connected in-between might be neither L nor TI.) time-varying filters is the topic of the email. �your VA paper along with others (like Jean Laroche) speak to it. �there are other LTI forms than either emulating a circuit or using simple biquads. �there's Hal's SVF (oh, that's emulating a circuit, sorta, but Hal is doing the "Naive" emulation of s^(-1)) and, what i would recommend, is the use of 2nd-order Lattice (if you have floating point) or Normalized Ladder (if you're doing this in fixed point) if you want to wildly modulate resonant frequency. �that's actually pretty commonly known in the industry. a "transfer function" is not enough information to fully define a system unless other assumptions are made (like "observability" or "controllability"). �that's why the general state-variable system (Hal's title is a little bit of a misnomer), ya know with the A, B, C, D matrices, exists to generalize it. �i'm pretty confident that any *linear* circuit (but possibly time-varying) you toss up there, with either gooder or badder emulation of the reactive elements, will come out as this generalized state-variable system. � but with some coefficients that can vary. �like in�http://control.ucsd.edu/mauricio/courses/mae280a/lecture8.pdf . �i couldn't easily find a discrete-time version on the web. �you might notice that there *is* a concept of a time-variant impulse response h(t, tau) (if it were LTI, h(t, tau) = h(t-tau)). �it's the impulse response, h(t), responding to a unit impulse applied at time tau. �fix tau and you have an h(t). �if you have an h(t), then you also have an H(s) (or in general an H(s,tau)) and i might call that a "transfer function". �but it's a time-varying transfer function and if it varies wildly, you can't use Fourier analysis at all. �but if it varies slowly enough, you can use Fourier analysis, at least to the point of discussing frequency response and the behavior of the system for short periods of time. � -- r b-j � � � � � � � � �r...@audioimagination.com "Imagination is more important than knowledge." �
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