Re: Matched Lowpass Filter
Posted: Fri Mar 06, 2020 1:56 am
Sweet , testing these.
Thanks martin
Thanks martin
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if x<1000
b0 = -2.8877914930158800E-17*x^4 + 5.1505099601836300E-13*x^3 - 8.3042766124760100E-09*x^2 + 1.1658923888554000E-04*x + 4.7538137317132600E-09;
b1 = -8.5798500741765000E-18*x^4 + 1.5075985241148900E-13*x^3 - 1.8436891078309800E-09*x^2 + 2.5886403730853200E-05*x + 1.4813928303349300E-09;
a1 = -1.0000210773722100E+00 * exp(-1.4259268000113900E-04*x);
else
b0 = -1.4099442035756000E-30 * x^7 + 1.0017110602452500E-25 * x^6 - 2.5601690530276300E-21 * x^5 + 2.3521737834624400E-17 * x^4 + 1.5572294695099200E-13 * x^3 - 7.1802325915484600E-09 * x^2 + 1.1519383331259800E-04 * x + 4.0299292935725700E-04;
b1 = -4.7895187177706000E-30 * x^7 + 3.6547584697795600E-25 * x^6 - 1.0692798201684300E-20 * x^5 + 1.4808481293564600E-16 * x^4 - 9.5370681840518000E-13 * x^3 + 1.8314251162411300E-09 * x^2 + 2.1044667135830600E-05 * x + 1.4837308218941300E-03;
a1 = -6.1994629213463400E-30 * x^7 + 4.6564695300249300E-25 * x^6 - 1.3252967254712400E-20 * x^5 + 1.7160655077027700E-16 * x^4 - 7.9798387145426300E-13 * x^3 - 5.3488074753069200E-09 * x^2 + 1.3623850044842700E-04 * x - 9.9811327624874200E-01;
end if
juha_tp wrote:Could this type of implementation give any advantages in real time applications ... (at least in case of (Butterworth) LP and HP filters with fixed Q)?
martinvicanek wrote:In principle, yes. Polynomial approximatios may be very efficient and have a smaller footprint than lookup tables. Personally I wonder what application would require such an extraordinarily accurate match to the analog magnitude response of a first order filter? Polynomials of seventh(!) degree, hmmm. Then, as you note, higher order filters have more independent parameters e.g. Q in addition to the cutoff frequency, which makes a polynomial fit a lot messier.