since you manually adjust the coefficient, i wanted to see the difference with coefficient adjusted/optimised by a computer. I update the calc using X from -0.5 to 0.5 with X = (x-0.5)*Pi The coefficient i get are really different from yours (when considering the Pi factor between them).
I update you patch with this coefs. I don't understand why, but your coefs works better for low frequency. so, nothing better here, but I still think it's worth sharing, in case i'm not the only one wondering... also, there was a typo in my original mail, it's not a linear regression, but a polynomial regression (since the result was obviously polynomial) cheers c Le 19/10/2016 à 15:06, katja a écrit :
Changing the thread title to reflect the new approach. Extract of the original thread; - I suggested using iemlib's hi pass filter recipe to improve frequency response of [hip~] - Christof Ressi pointed to formula in http://www.arpchord.com/pdf/coeffs_first_order_filters_0p1.pdf - this formula calculates feedback coefficient k = (1 - sin(a)) / cos(a) where a = 2 * pi * fc / SR - the filter implementation is y[n] = (x[n] - x[n-1]) * (1 + k) / 2 + k * y[n-1] - following convention in d_filter.c (and pd tilde classes in general), trig functions should best be approximated - Cyrille provided libre office linear regression result for (1-sin(x))/cos(x) Thanks for the useful infos and discussion. My 'math coach' suggested using odd powers of -(x-pi/2) in an approximation polynomial for (1-sin(x))/cos(x). The best accuracy/performance balance I could get is with this 5th degree polynomial: (-(x-pi/2))*0.4908 - (x-pi/2)^3*0.04575 - (x-pi/2)^5*0.00541 Using this approximation in the filter formula, response at cutoff frequency is -3 dB with +/-0.06 dB accuracy in the required range 0 < x < pi. It can be efficiently implemented in C, analogous to an approximation Miller uses in [bp~]. So that is what I'll try next. Attached patch hip~-models.pd illustrates and compares filter recipes using vanilla objects: - current implementation, most efficient, accuracy +/- 3 dB - implementation with trig functions, least efficient, accuracy +/- 0.01 dB - implementation with approximation for trig functions, efficient, accuracy +/- 0.06 dB A note on efficiency: coefficients in [hip~] are only recalculated when cutoff frequency is changed. How important is performance for a function rarely called? I'm much aware of the motto 'never optimize early', yet I spent much time on finding a fast approximation, for several reasons: it's a nice math challenge, instructive for cases where performance matters more, and I want to respect Miller's code efficiency when proposing a change. Today pd is even deployed on embedded devices so the frugal coding approach is still relevant. After 20 years. Katja On Tue, Oct 18, 2016 at 10:28 AM, cyrille henry <[email protected]> wrote: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 _______________________________________________ [email protected] mailing list UNSUBSCRIBE and account-management -> https://lists.puredata.info/listinfo/pd-list
hip~-models.pd
Description: application/puredata
polynomial_regression.ods
Description: application/vnd.oasis.opendocument.spreadsheet
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