Le 18/10/2016 à 00:47, katja a écrit :
The filter recipe that Christof pointed to was easy to plug into the C code of [hip~] and works perfectly. But when looking further in d_filter.c I came across an approximation function 'sigbp_qcos()' used in the bandpass filter. It made me realize once more how passionate Miller is about efficiency. I'm not going to make a fool of myself by submitting a 'fix' using two trig functions to calculate a filter coefficient when a simple approximation could do the job. So that is what I'm now looking into, with help of a math friend: an efficient polynomial approximation for (1-sin(x))/cos(x).
according to libre office linear regression, for x between 0 and Pi, (1-sin(x))/cos(x) is about : -0.057255x³ + 0.27018x² - 0.9157x + 0.99344 the calc is in attachment, if you want to tune the input source or precision. cheers c
Katja On Sat, Oct 15, 2016 at 4:59 PM, katja <katjavet...@gmail.com> wrote:Thanks for your pointers Christof. The recipe you mention from arpchord.com is different than iemlib's, but yields identical normalization and feedback coefficients, thus the same beautiful response. As you say, what's in the textbooks is common knowledge and can be used by everyone. Now I'll try to get the same result in C. By the way, [iemlib/hp~] seems to recalculate coefficients for every dsp vector which explains the higher CPU load. Katja On Sat, Oct 15, 2016 at 1:59 PM, Christof Ressi <christof.re...@gmx.at> wrote:If iemlib's license allows to use the recipe in BSDIMHO, the correct formular for the cutoff frequency below (which I guess is also used in [hp1~] since the frequency response is the same) is 'common knowledge', so I don't think you'd have to pay attention to any licence.Gesendet: Samstag, 15. Oktober 2016 um 13:52 Uhr Von: "Christof Ressi" <christof.re...@gmx.at> An: katja <katjavet...@gmail.com>, "Miller Puckette" <m...@ucsd.edu> Cc: pd-list <pd-l...@iem.at> Betreff: Re: [PD] could vanilla borrow iemlib's hi pass filter recipe?But coefficients aren't recalculated so often, therefore this difference will be negligible.That's a good point. You're right that both involve a feedback and feedforward, so I'm wondering why [hp1~] needs more CPU... otherwise, iemlib's filters are very efficient. Anyway, I researched a bit and found the reason why the frequency response of Pd filters seems 'wrong': Miller uses a formular for calculating the cutoff frequency which is taken from analog filters but is not really adequate for digital filters since it doesn't reflect the cyclic nature of the digital domain (although you can see it in some articles on digital filters). Let's take [hip~] as an example: the formular for a 1-pole 1-zero highpass goes: y[n] = (x[n] - x[n-1]) * (1 + k) / 2 + k * y[n-1] Miller calculates the position of the pole with k = 1 - (fc * 2*pi / SR). The correct formular, however (if you want the frequency response to be zero at Nyquist!), would be k = (1-sin(a))/cos(a), where a = fc * 2*pi / SR. You can find it here: http://www.arpchord.com/pdf/coeffs_first_order_filters_0p1.pdf BTW, the reason why [hip~] seems to get stuck at 7018 Hz is because Miller clips the coefficient below 0, so it never reaches -1 (where the gain would be all zero). Also, there is another approximation with a similiar behaviour, which goes like this: k = e^(-2*pi*fc/SR). I could find it here: http://www.dspguide.com/ch19/2.htm Here, the pole can only move from 1 to 0 and doesn't ever reach -1 as well. Now, is the behaviour of [hip~] 'wrong'? If you define at 1-pole 1-zero high pass filter as something which passes everything at fc = DC and blocks everything at fc = Nyquist, then I'd say yes. If it should roughly model an analogue filter (where the cutoff frequency can go up to infinity) for low cutoff frequencies only, then I'd say no. Also, as I tried to point out, this issue with the cutoff frequency is true for all Pd filters! So I think this behaviour should either be changed (great, if Katja is willing to submit a patch!) or documented in the help patch (gain is not 0 at Nyquist!). I'm not an engineer or any expert on filter design. It's just my two cents :-) ChristofGesendet: Samstag, 15. Oktober 2016 um 11:39 Uhr Von: katja <katjavet...@gmail.com> An: "Christof Ressi" <christof.re...@gmx.at> Cc: pd-list <pd-l...@iem.at> Betreff: Re: [PD] could vanilla borrow iemlib's hi pass filter recipe? I'm pretty confident [hip~] would not loose its efficiency when using iemlib's recipe. Both hi pass filters have a feed forward and feedback component, with coefficients for normalization and feedback. Calculation of these coefficients is a bit more involved with iemlib's recipe, using trig functions. But coefficients aren't recalculated so often, therefore this difference will be negligible. To reassure, it is not my intention to spark another 'what's wrong with pd' thread. If iemlib's license allows to use the recipe in BSD code I'll try patch the C of [hip~] and submit on the tracker for review. Who knows, it may be a no-brainer. Katja On Sat, Oct 15, 2016 at 2:34 AM, Christof Ressi <christof.re...@gmx.at> wrote:There are a number of big problems with all build-in filters in Pd (expect for the raw filters). Problem number 1: [lop~] and [hip~] both use a weird (you could also say: wrong) formula for the cutoff frequency which makes them gradually converge to a fixed output state (reached by about 7000 Hz). The same is true for [vcf~] and [bp~] with Q <= 1. Therefore the actual cutoff frequency is only correct for very low frequencies and approximately gets more and more off until it doesn't move at all. Problem number 2: [bp~] and [vcf~] don't have zeros at DC and Nyquist. For low Q values, the slope is different for each side and changes with frequency. Problem number 3: the gain at the center frequency is not 1 for both [bp~] and [vcf~]. It rather depends on frequency and Q. [bp~] even has has a gain of 2 for Q <= 1! I did some FFT plots, see the attachment. I remember Miller saying somewhere that these filters are not designed for high cutoff frequencies - but even for low frequencies, the behaviour of [bp~] and [vcf~] is horrible. I can see these filters are mere approximations to reduce CPU usage. [hip~] is indeed much more efficient than iemlib's [hp1~], so it's well suited for DC removal (but not much else). [bp~] only is a little bit more CPU friendly than iemlib's [bp2~] - but the latter one has a correct and stable frequency response. [vcf~], however, is a real CPU sucker!!! 100 [vcf~] objects need 3,40% on my laptop whereas 100 of iemlib's [vcf_bp2~] only need 1,80%! But you have to consider that [vcf_bp2~] not only acts correctly but lets you set the Q at audio rate. The high CPU usage of [vcf~] seems like a bug to me... I only use the vanilla filters for the most basic stuff like DC removal and smoothing. I guess these are the use cases which Miller had in mind and that way [lop~] and [hip~] have their justification (although there should be some more warning about the 'wrong' frequency response in the help file). But [bp~] and [vcf~] are almost unusable IMHO and should probably be replaced by better filters in the future (while keeping the old ones for compatibility reasons). ChristofGesendet: Freitag, 14. Oktober 2016 um 23:51 Uhr Von: katja <katjavet...@gmail.com> An: pd-list <pd-l...@iem.at> Betreff: [PD] could vanilla borrow iemlib's hi pass filter recipe? In pd 0.47.1 [hip~] is still not perfect. Attenuation at cutoff is not constant over the frequency range: -6 dB with cutoff=SR/8, -3 dB with cutoff=SR/4, 0 DB with cutoff=SR/2. In contrast, iemlib's [hp1~] has -3 dB at cutoff consistently. Could vanilla pd implement iemlib's hipass filter recipe? I don't know if the license also covers the math. Documentation in https://git.iem.at/pd/iemlib/tree/master points to external literature for part of the math (bilinear transform). I've implemented the recipe with vanilla objects for comparison, see attached. 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