Re: [music-dsp] Introductory literature for loudspeaker predistortion
On Mar 3, 2014, at 8:14 AM, Marco Lo Monaco wrote: > Hello jerry, > Klippel is one of the most experienced in the field and I believe that > looking thru his literature (papers) you will find a lot of inspiration. Yes, I thought to look at Klippel's web site, and indeed there are a lot of papers listed there. Unfortunately, I think most or all of them are not suitable for a senior project for being too advanced. > AFAIK he uses a generic non linear dynamic model and performs various > techniques of identification, among the others Volterra (which actually can > emulate only mild nonlinearities). > I remember there is a paper by him using NARMAX method which could be > interesting for a university project. > Generally speaking, once you have an identified model, by applying inversion > you can in theory compensate also all nonlinarities: inverting a linear > system is pretty standard, it couldn’t be so easy for a non linear. > > For all of your questions: > 1) How dependent on the signal is a nonlinear model for a speaker? > A: Well, I could say a lot on large signal (speaker breakup), not so much > for small ones (only freq response taken into account). I would define it a > nonlinear process so the question maybe is too generic. > > 1) Is it possible to do some good by measuring a single nonlinearity curve > for the loudspeaker under some condition and (assuming it is invertible) > applying the inverse nonlinearity as predistortion? > A: Technically yes but AFAIK a static nonlinearity is too simple also > because of difficulties of keeping the cone always on axis far large values > of voltage applied. While on its dynamic behavior the nonlinearity is thus > different (take that as an intuition thought). > > 2) Surely providing motion information (e.g. an accelerometer attached to > the cone) into a feedback loop would help to linearize things. Some > commercial subwoofers do this. > A: Klippel uses a laser vibrometer, which I believe is quite standard for > parameter estimation of the model. I guess that an accelerometer is good for > low bandwidth signal (subwoofers) but not for mid range/tweeters. > > 4) The first thing I would try is drive a loudspeaker with a sine or > triangle and look at the input-output curve on an x-y oscilloscope. If the > line isn't straight then there is distortion and if the "line" opens up then > there is hysteresis -> memory. Right? > A: Yes you would certainly see some memory effect for large signals applied, > I bet. Ah, I wrote too quickly. What I said might be true, but the "line" (actually a Lissajous figure) will open up even with no distortion but simply a phase shift. > > Pls take my thoughts as they are, because I never worked on nonlinear > speaker emulation, even if is something I would love to do in the future. > > Ciao > > Marco I met with the students today as kind of an informal advisor. Their project is not what I originally understood it to be. They are actually putting an adaptive LMS filter in series with the loudspeaker and trying to get the combination to match a target function which is, during training, connected in parallel to the series connection of LMS and loudspeaker--pretty standard stuff, but correcting only linear distortion. I think if they get interested in correcting for nonlinear things, maybe a sensible project would be to attach an accelerometer to the cone and close a loop on it. Thanks for your thoughts. Jerry > > -Messaggio originale- > Da: music-dsp-boun...@music.columbia.edu > [mailto:music-dsp-boun...@music.columbia.edu] Per conto di Jerry > Inviato: venerdì 28 febbraio 2014 00:50 > A: A discussion list for music-related DSP > Oggetto: [music-dsp] Introductory literature for loudspeaker predistortion > > Does anyone know the literature for loudspeaker predistortion--literature > appropriate for senior-year electrical engineering students? (That's not > me.) I suppose this would rule out fancy stuff like Volterra series > inversion and use of psychoacoustic metrics. > > How dependent on the signal is a nonlinear model for a speaker? > > Is it possible to do some good by measuring a single nonlinearity curve for > the loudspeaker under some condition and (assuming it is invertible) > applying the inverse nonlinearity as predistortion? > > Surely providing motion information (e.g. an accelerometer attached to the > cone) into a feedback loop would help to linearize things. Some commercial > subwoofers do this. > > The first thing I would try is drive a loudspeaker with a sine or triangle > and look at the input-output curve on an x-y oscilloscope. If the line isn't > straight then there is distortion and if the "line" opens up then there is > hysteresis -> memory. Right? > > I'm vaguely aware of the work of Klippel http://www.klippel.de/ but not at > all familiar with it. > > I'm just looking for some information to feed the senior projects, not > change the world. > > Jerry > -- > dupswapdrop
Re: [music-dsp] Iterative decomposition of an arbitrary frequency response by biquad IIR
On 5/03/2014 2:27 PM, Sampo Syreeni wrote: Pretty sure that literature has to contain the relevant algorithms if used with just a single resonance. I never looked at rational function fitting, but this would be easy enough to try: http://www.mathworks.com.au/help/rf/rationalfit.html The link cites: B. Gustavsen and A. Semlyen, "Rational approximation of frequency domain responses by vector fitting," IEEE Trans. Power Delivery, Vol. 14, No. 3, pp. 1052–1061, July 1999. 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
Re: [music-dsp] Iterative decomposition of an arbitrary frequency response by biquad IIR
On 2014-03-05, Ross Bencina wrote: Pretty sure that the oft-cited Knud Bank Christensen paper does LMS fit of a biquad over an arbitrary sampled frequency response. If not, then Serra and the rest of the FOF folks did implementations where formants were implemented with fitted biquads. Pretty sure that literature has to contain the relevant algorithms if used with just a single resonance. Or then just go with second order linear prediction from the impulse response, and transform back to biquad coefficient space. -- Sampo Syreeni, aka decoy - de...@iki.fi, http://decoy.iki.fi/front +358-40-3255353, 025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2 -- 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] Iterative decomposition of an arbitrary frequency response by biquad IIR
On 5/03/2014 7:56 AM, Ethan Duni wrote: Seems like somebody somewhere should have already thought through the problem of matching a single biquad stage to an arbitrary frequency response - anybody? Pretty sure that the oft-cited Knud Bank Christensen paper does LMS fit of a biquad over an arbitrary sampled frequency response. In the paper they match a low-order analog filter response curve, but from memory the technique breaks the target response into frequency bands, as such it should be usable for an arbitrary response. Maybe that's not the most efficient approach for a real-time situation, but it will give you an optimal fit. Knud Bank Christensen, "A Generalization of the Biquadratic Parametric Equalizer," AES 115, 2003, New York. 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
Re: [music-dsp] music-dsp Digest, Vol 123, Issue 9
On 3/4/14 11:53 AM, Ethan Duni wrote: LDS, LSD... you do the math... ya. too much of the latter for me, i'm afraid. i've risked death on it. on my motorcycle in the '80s. https://maps.google.com/maps?f=q&source=s_q&hl=en&sll=41.87985,-87.61734&sspn=0.020002,0.045447&vpsrc=6&t=h&ie=UTF8&ll=41.87985,-87.61734&spn=0.020002,0.045447&z=15&ei=vEsWU-zYOcHMsgTvhIKIBw&pw=2 E On Mar 4, 2014 8:45 AM, "robert bristow-johnson" wrote: On 3/4/14 11:37 AM, gjberc...@charter.net wrote: On Tue, 04 Mar 2014 11:28:37 -0500, robert bristow-johnson wrote: as far as i know there is the prony method. the yulewalk. and Greg Berchin's FLDS. ***PLEASE*** ... it's FDLS "Frequency Domain Least Squares", not FLDS. FLDS is Fundamentalist Church of Latter Day Saints, something very different. gack!! Greg, i'm sorry. it's not the first time i made that very same mistake. fDls, fDls... i'll get it eventually. L8r, -- 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 -- 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] Iterative decomposition of an arbitrary frequency response by biquad IIR
Seems to me that you could just reformulate an EM algorithm to work directly on the actual (magnitude) responses of the biquad stages, and so bypass the step of converting from a Gaussian response to the actual biquad response (along with its attendant error). The only obvious wrinkle that occurs to me is the possibility of zeros on the unit circle, which would result in a non-differentiable magnitude response at those points. But maybe that could be avoided by using an "amplitude response" (i.e., signed magnitude response) type formulation? But likewise, using a Gaussian approximation seems to assume that there are no zeros of interest anyway. Alternatively, you can always just use brute-force techniques for the maximization step which don't require differentiation. But really I think Sampo had the right of it earlier: the "correct" way to do this is to apply ARMA techniques to get a rational approximation of the desired frequency response, and then just factor that down to whatever topology you want. The rub is if you want to do this in real time, in which case the filter factorization becomes problematic. That said, some kind of recursive biquad-matching type approach seems like it should be relatively straightforward and work acceptably if not pushed too hard (i.e., relatively low-order approximations, no perverse target responses). Seems like somebody somewhere should have already thought through the problem of matching a single biquad stage to an arbitrary frequency response - anybody? E On Tue, Mar 4, 2014 at 12:15 PM, Mike wrote: > Mike wrote: >> >You could try pretending they're Gaussian shaped (and then translate the >> >sigma to Q), >> What's "they" in the comparison, I mean are we talking Frequency Domain >> here, where a band filters characteristic pass band curve is to be >> replaced by a statistics integral ? Doesn't make much sense to me (and I >> know all the concepts mentioned pretty fundamentally well). >> > > The "they" would be 2nd-order band-pass IIR blocks, and the idea would be > to convert the desired frequency response into a set of data points (the > density could even be adjusted to give some portions of the response more > weight), and then fit N Gaussians, and then approximate each with the > 2nd-order block. > > > > -- > 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] Iterative decomposition of an arbitrary frequency response by biquad IIR
Mike wrote: >You could try pretending they're Gaussian shaped (and then translate the >sigma to Q), What's "they" in the comparison, I mean are we talking Frequency Domain here, where a band filters characteristic pass band curve is to be replaced by a statistics integral ? Doesn't make much sense to me (and I know all the concepts mentioned pretty fundamentally well). The "they" would be 2nd-order band-pass IIR blocks, and the idea would be to convert the desired frequency response into a set of data points (the density could even be adjusted to give some portions of the response more weight), and then fit N Gaussians, and then approximate each with the 2nd-order block. -- 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] Iterative decomposition of an arbitrary frequency response by biquad IIR
On Tue, 04 Mar 2014 13:49:43 -0500, Uli Brueggemann wrote: >>Hello Greg, >> >>I've unsuccessfully tried to find more about FDLS. >>Can you please give me a tip or even send me some info by PM? >> >>- Uli PM sent. - Greg = Everybody has their moment of great opportunity in life. If you happen to miss the one you care about, then everything else in life becomes eerily easy. -- Douglas Adams -- 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] Negative PCA coefficients
On Mar 4, 2014 1:16 AM, "Linda Seltzer" wrote: > And when some components have very small absolute > values does that mean they can be omitted in an image of the component? > Linda Seltzer > Small values should not be simply omitted. It's sort of an effect size consideration. Not all variables will have similar scales--think about units. Suppose one of your variables is distance--should you get the same basic relationship if you measure it in meters or kilometers? Since you're doing an experiment, try taking one variable and multiplying it by a factor. Chuck -- 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] Negative PCA coefficients
Negative coefficients are like a negative correlation. I say "like", because PCA gives you vectors of associated variables along which the variance in the data is decomposed. That's not exactly the same as correlation. The other part to pay attention is the eigenvalues. The largest components (closest to 1) are the vectors of covariance which have the most predictive value. An entire vector with negative values should never appear. The sign should be interpreted as the direction of variance in the factor relative to other variables. Chuck On Mar 4, 2014 1:16 AM, "Linda Seltzer" wrote: > Even after reading math books and journal articles, I find that I never > really understand an algorithm unless I work on it with actual data and > software. Today I ran a principal component analysis in Matlab and the > resulting matrix contained negative coefficients. The rows are the > components and the columns are the variables. I would understand positive > components as weights, with the smallest weights meaning those variables > do not contribute greatly to the component. But what do negative > coefficients mean? And when some components have very small absolute > values does that mean they can be omitted in an image of the component? > Linda Seltzer > > > -- > 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] music-dsp Digest, Vol 123, Issue 9
Hello Greg, I've unsuccessfully tried to find more about FDLS. Can you please give me a tip or even send me some info by PM? - Uli 2014-03-04 17:37 GMT+01:00 : > On Tue, 04 Mar 2014 11:28:37 -0500, robert bristow-johnson wrote: > > >>as far as i know there is the prony method. the yulewalk. and Greg > >>Berchin's FLDS. > > ***PLEASE*** ... it's FDLS "Frequency Domain Least Squares", not FLDS. > > FLDS is Fundamentalist Church of Latter Day Saints, something very > different. > > - Greg Berchin > > = > > Everybody has their moment of great opportunity in life. > If you happen to miss the one you care about, then > everything else in life becomes eerily easy. > > -- Douglas Adams > -- > 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] music-dsp Digest, Vol 123, Issue 9
On 3/4/14 11:37 AM, gjberc...@charter.net wrote: On Tue, 04 Mar 2014 11:28:37 -0500, robert bristow-johnson wrote: as far as i know there is the prony method. the yulewalk. and Greg Berchin's FLDS. ***PLEASE*** ... it's FDLS "Frequency Domain Least Squares", not FLDS. FLDS is Fundamentalist Church of Latter Day Saints, something very different. gack!! Greg, i'm sorry. it's not the first time i made that very same mistake. fDls, fDls... i'll get it eventually. L8r, -- 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] music-dsp Digest, Vol 123, Issue 9
LDS, LSD... you do the math... E On Mar 4, 2014 8:45 AM, "robert bristow-johnson" wrote: > On 3/4/14 11:37 AM, gjberc...@charter.net wrote: > >> On Tue, 04 Mar 2014 11:28:37 -0500, robert bristow-johnson wrote: >> >> as far as i know there is the prony method. the yulewalk. and Greg Berchin's FLDS. >>> ***PLEASE*** ... it's FDLS "Frequency Domain Least Squares", not FLDS. >> >> FLDS is Fundamentalist Church of Latter Day Saints, something very >> different. >> > > gack!! > > Greg, i'm sorry. it's not the first time i made that very same mistake. > > fDls, fDls... i'll get it eventually. > > L8r, > > > -- > > 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] music-dsp Digest, Vol 123, Issue 9
On Tue, 04 Mar 2014 11:28:37 -0500, robert bristow-johnson wrote: >>as far as i know there is the prony method. the yulewalk. and Greg >>Berchin's FLDS. ***PLEASE*** ... it's FDLS "Frequency Domain Least Squares", not FLDS. FLDS is Fundamentalist Church of Latter Day Saints, something very different. - Greg Berchin = Everybody has their moment of great opportunity in life. If you happen to miss the one you care about, then everything else in life becomes eerily easy. -- Douglas Adams -- 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] Iterative decomposition of an arbitrary frequency response by biquad IIR
On 3/4/14 11:19 AM, Theo Verelst wrote: robert bristow-johnson wrote: You put probes in the ground, set of a bar of dynamite, and measure the seismic response. Then take a lot of assumptions, and try to invert those measurments into a soil sediment picture, as to find oil... still haven't connected that to decomposition of an arbitrary frequency response into a rational (in z) IIR transfer function from which biquads can be factored out. Allright, maybe to far fetched example, certainly in it's execution not first year stuff. it just interests me, and it suggests a searching for system responses, that I suppose is in the thinking line of the question, but I don't know that for sure. I didn't get the part where the frequency response is a given, I mean, how is that given (and where does that come from). And if indeed a certain response is to be implemented as a digital filter, why does phase not matter, too ? perhaps you draw it out with a mouse. or your finger on an iPad. or piecewise linear with breakpoints (that you can slide around with your finger). as far as i know there is the prony method. the yulewalk. and Greg Berchin's FLDS. or fiddle around with the poles and zeros manually. i dunno. -- 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] Iterative decomposition of an arbitrary frequency response by biquad IIR
theo verelst wrote: I didn't get the part where the frequency response is a given, I mean, how > is that given (and where does that come from). And if indeed a certain > response is to be implemented as a digital filter, why does phase not > matter, too ? > Assume a frequency response of a speaker to be equalized. The response may be smoothed and described by a minimum phase pulse response. - Uli -- 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] Iterative decomposition of an arbitrary frequency response by biquad IIR
robert bristow-johnson wrote: You put probes in the ground, set of a bar of dynamite, and measure the seismic response. Then take a lot of assumptions, and try to invert those measurments into a soil sediment picture, as to find oil... still haven't connected that to decomposition of an arbitrary frequency response into a rational (in z) IIR transfer function from which biquads can be factored out. Allright, maybe to far fetched example, certainly in it's execution not first year stuff. it just interests me, and it suggests a searching for system responses, that I suppose is in the thinking line of the question, but I don't know that for sure. I didn't get the part where the frequency response is a given, I mean, how is that given (and where does that come from). And if indeed a certain response is to be implemented as a digital filter, why does phase not matter, too ? T. -- 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] Iterative decomposition of an arbitrary frequency response by biquad IIR
On 3/4/14 11:05 AM, Theo Verelst wrote: robert bristow-johnson wrote: On 3/4/14 9:37 AM, Theo Verelst wrote: Ross Bencina wrote: Since people are throwing out random suggestions, ... I have not made any random suggestions thus far. Undergrad univ. EEs can recognize easily (if they're a bit good and are in a proper eduction institute) what I've mentioned here. i haven't easily recognized the "drilling for oil" thing. but i only went to the University of North Dakota and Northwestern. You put probes in the ground, set of a bar of dynamite, and measure the seismic response. Then take a lot of assumptions, and try to invert those measurments into a soil sediment picture, as to find oil... still haven't connected that to decomposition of an arbitrary frequency response into a rational (in z) IIR transfer function from which biquads can be factored out. -- 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] Iterative decomposition of an arbitrary frequency response by biquad IIR
robert bristow-johnson wrote: On 3/4/14 9:37 AM, Theo Verelst wrote: Ross Bencina wrote: Since people are throwing out random suggestions, ... I have not made any random suggestions thus far. Undergrad univ. EEs can recognize easily (if they're a bit good and are in a proper eduction institute) what I've mentioned here. i haven't easily recognized the "drilling for oil" thing. but i only went to the University of North Dakota and Northwestern. You put probes in the ground, set of a bar of dynamite, and measure the seismic response. Then take a lot of assumptions, and try to invert those measurments into a soil sediment picture, as to find oil... -- 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] Iterative decomposition of an arbitrary frequency response by biquad IIR
On 3/4/14 9:37 AM, Theo Verelst wrote: Ross Bencina wrote: Since people are throwing out random suggestions, ... I have not made any random suggestions thus far. Undergrad univ. EEs can recognize easily (if they're a bit good and are in a proper eduction institute) what I've mentioned here. i haven't easily recognized the "drilling for oil" thing. but i only went to the University of North Dakota and Northwestern. -- 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] Iterative decomposition of an arbitrary frequency response by biquad IIR
There is no simple method that I've ever heard of, but I think this problem is a good candidate to be solved as an optimization problem. I actually wrote some MATLAB scripts some time ago to design a filterbank based on a cascade of biquads without needing to use anything fancier than the fmincon function in MATLAB. The filters had both amplitude and group delays defined arbitrarily. The algorithm was iterative and not terribly fast, but converged to good filters in a decent amount of time. Unfortunately I cannot share the code as it is proprietary. There are fancier methods based on convex optimization (e.g., the one detailed in this thesis http://scholar.uwindsor.ca/cgi/viewcontent.cgi?article=1431&context=etd). If you are interested in doing something like this, I would suggest using optimization packages such as SeDuMi and CVX. Hope it helps -- João Felipe Santos On Tue, Mar 4, 2014 at 9:59 AM, Uli Brueggemann wrote: > Thanks so far for the different proposals. > I must admit that I do not have much skills with Matlab. > And it seems the proposals require all steep learning curve. > > Maybe the problem I like to solve can be described with an example: > > Let's assume a series of two biquad peaking filters, first with f1=100 Hz, > Q1=1, gain1=6 dB, second with f2=1000 Hz, Q2=1, gain2=-3 dB > The amplitude response of the series is given. > Now I like to decompose the given response back to biquad filters = finding > the above given parameters. > > This is a most ideal case as the given response is generated by biquads. Of > course the series may consist of even more biquads and include all > different types defined in the EQ cookbook. > > Furthermore the problem gets even worse if the given frequency response is > arbitrary but smooth. > Then in my understanding of course some best fit and error consideration > has to take place. > > So my question is: is there a simple approach? > As already said I do not know much about Matlab and I would like to write > my own code. > > - Uli > > > > > 2014-03-04 15:37 GMT+01:00 Theo Verelst : > > > Ross Bencina wrote: > > > >> Since people are throwing out random suggestions, ... > >> > > > > I have not made any random suggestions thus far. Undergrad univ. EEs can > > recognize easily (if they're a bit good and are in a proper eduction > > institute) what I've mentioned here. > > > > It's just that a certain group of people, which apparently has also been > > active to change the democratically founded Wikipedia into some > "movement" > > propagation pamphlet, unhindered by scruples about mathematical and > > theoretical correctness, is so eager to mean something, that somehow > > subjects grow on other trees than reasonableness and engineering > soundness. > > > > Once again, system theory, especially linear system theory is there > > already for centuries. Trying to crack non-linear systems is to an extend > > possible in EE and Physics, but hard to do. That's not a reason to goof > off > > in all kinds of directions, forgetting about sampling theory, laws of > > Linearity, rules for applying convolution (like initial conditions being > > zero, and there's no memory in the convolutor), or, like here, suggesting > > all kinds of brannish system approximations clearly without feeling > > sufficiently stupid in trying to apply the actual higher math kinds since > > Einstein c.s. in such ridiculous way. > > > > So: statistics aren't the same as filters, frequencies aren't the same a > > place-vectors, conditional probabilities aren't the same as singular > value > > decompositions, and drilling for digital furs is funny, but usually > > hopeless. > > > > > > T. > > > > -- > > 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] Iterative decomposition of an arbitrary frequency response by biquad IIR
Thanks so far for the different proposals. I must admit that I do not have much skills with Matlab. And it seems the proposals require all steep learning curve. Maybe the problem I like to solve can be described with an example: Let's assume a series of two biquad peaking filters, first with f1=100 Hz, Q1=1, gain1=6 dB, second with f2=1000 Hz, Q2=1, gain2=-3 dB The amplitude response of the series is given. Now I like to decompose the given response back to biquad filters = finding the above given parameters. This is a most ideal case as the given response is generated by biquads. Of course the series may consist of even more biquads and include all different types defined in the EQ cookbook. Furthermore the problem gets even worse if the given frequency response is arbitrary but smooth. Then in my understanding of course some best fit and error consideration has to take place. So my question is: is there a simple approach? As already said I do not know much about Matlab and I would like to write my own code. - Uli 2014-03-04 15:37 GMT+01:00 Theo Verelst : > Ross Bencina wrote: > >> Since people are throwing out random suggestions, ... >> > > I have not made any random suggestions thus far. Undergrad univ. EEs can > recognize easily (if they're a bit good and are in a proper eduction > institute) what I've mentioned here. > > It's just that a certain group of people, which apparently has also been > active to change the democratically founded Wikipedia into some "movement" > propagation pamphlet, unhindered by scruples about mathematical and > theoretical correctness, is so eager to mean something, that somehow > subjects grow on other trees than reasonableness and engineering soundness. > > Once again, system theory, especially linear system theory is there > already for centuries. Trying to crack non-linear systems is to an extend > possible in EE and Physics, but hard to do. That's not a reason to goof off > in all kinds of directions, forgetting about sampling theory, laws of > Linearity, rules for applying convolution (like initial conditions being > zero, and there's no memory in the convolutor), or, like here, suggesting > all kinds of brannish system approximations clearly without feeling > sufficiently stupid in trying to apply the actual higher math kinds since > Einstein c.s. in such ridiculous way. > > So: statistics aren't the same as filters, frequencies aren't the same a > place-vectors, conditional probabilities aren't the same as singular value > decompositions, and drilling for digital furs is funny, but usually > hopeless. > > > T. > > -- > 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] Iterative decomposition of an arbitrary frequency response by biquad IIR
Ross Bencina wrote: Since people are throwing out random suggestions, ... I have not made any random suggestions thus far. Undergrad univ. EEs can recognize easily (if they're a bit good and are in a proper eduction institute) what I've mentioned here. It's just that a certain group of people, which apparently has also been active to change the democratically founded Wikipedia into some "movement" propagation pamphlet, unhindered by scruples about mathematical and theoretical correctness, is so eager to mean something, that somehow subjects grow on other trees than reasonableness and engineering soundness. Once again, system theory, especially linear system theory is there already for centuries. Trying to crack non-linear systems is to an extend possible in EE and Physics, but hard to do. That's not a reason to goof off in all kinds of directions, forgetting about sampling theory, laws of Linearity, rules for applying convolution (like initial conditions being zero, and there's no memory in the convolutor), or, like here, suggesting all kinds of brannish system approximations clearly without feeling sufficiently stupid in trying to apply the actual higher math kinds since Einstein c.s. in such ridiculous way. So: statistics aren't the same as filters, frequencies aren't the same a place-vectors, conditional probabilities aren't the same as singular value decompositions, and drilling for digital furs is funny, but usually hopeless. T. -- 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
