//! Butterworth filters: pre-calculated Second Order Sections coefficients for order 4 lowpass filters.
//! This file is autogenerated.
use crate::sos::SisoSosFilter;
use core::ops::Neg;
use num_traits::{FromPrimitive, MulAdd, Num, ToPrimitive};
pub const NUM_SECTIONS: usize = 2;
const NUM_INTERP_POINTS: usize = 100;
pub const MIN_CUTOFF_RATIO_F32: f64 = 0.005;
pub const MAX_CUTOFF_RATIO_F32: f64 = 0.4;
pub const MIN_CUTOFF_RATIO_F64: f64 = 0.0005;
pub const MAX_CUTOFF_RATIO_F64: f64 = 0.4;
// [dimensionless] Log base-10 of cutoff ratios, to improve float precision during interpolation
#[rustfmt::skip]
static LOG10_CUTOFF_RATIOS: [f64; NUM_INTERP_POINTS] = [-4.0, -3.963615555643152, -3.9272311112863036, -3.8908466669294555, -3.8544622225726077, -3.8180777782157596, -3.7816933338589114, -3.745308889502063, -3.708924445145215, -3.672540000788367, -3.636155556431519, -3.599771112074671, -3.5633866677178228, -3.5270022233609746, -3.4906177790041264, -3.454233334647278, -3.41784889029043, -3.3814644459335823, -3.345080001576734, -3.308695557219886, -3.2723111128630378, -3.2359266685061896, -3.199542224149342, -3.1631577797924937, -3.1267733354356455, -3.0903888910787973, -3.054004446721949, -3.017620002365101, -2.981235558008253, -2.9448511136514046, -2.9084666692945564, -2.8720822249377087, -2.8356977805808605, -2.7993133362240123, -2.7629288918671646, -2.7265444475103164, -2.6901600031534683, -2.65377555879662, -2.617391114439772, -2.5810066700829237, -2.5446222257260755, -2.5082377813692274, -2.471853337012379, -2.435468892655531, -2.3990844482986833, -2.362700003941835, -2.326315559584987, -2.289931115228139, -2.253546670871291, -2.217162226514443, -2.1807777821575947, -2.1443933378007465, -2.1080088934438983, -2.07162444908705, -2.035240004730202, -1.9988555603733542, -1.962471116016506, -1.9260866716596579, -1.8897022273028097, -1.8533177829459615, -1.8169333385891133, -1.7805488942322656, -1.7441644498754174, -1.7077800055185692, -1.671395561161721, -1.6350111168048729, -1.5986266724480247, -1.5622422280911765, -1.5258577837343288, -1.4894733393774806, -1.4530888950206324, -1.4167044506637843, -1.380320006306936, -1.343935561950088, -1.3075511175932402, -1.271166673236392, -1.2347822288795438, -1.1983977845226956, -1.1620133401658475, -1.1256288958089993, -1.089244451452151, -1.0528600070953034, -1.0164755627384552, -0.980091118381607, -0.9437066740247588, -0.9073222296679107, -0.8709377853110625, -0.8345533409542147, -0.7981688965973666, -0.7617844522405184, -0.7254000078836702, -0.689015563526822, -0.6526311191699739, -0.6162466748131261, -0.5798622304562779, -0.5434777860994298, -0.5070933417425816, -0.4707088973857334, -0.4343244530288852, -0.3979400086720376];
#[rustfmt::skip]
static SOS_TABLES: [[[f64; NUM_INTERP_POINTS]; 5]; NUM_SECTIONS] = [ [
[9.732916985803468e-15, 1.360660103371991e-14, 1.9021885432640173e-14, 2.659221504122345e-14, 3.717510894180601e-14, 5.1969254653792084e-14, 7.265021830356645e-14, 1.0156012441892176e-13, 1.4197276126578564e-13, 1.9846409398466525e-13, 2.774300805363836e-13, 3.8781032864984714e-13, 5.420993825175367e-13, 7.577599068156705e-13, 1.0591974021087391e-12, 1.480519448534309e-12, 2.069390964993145e-12, 2.892420541731133e-12, 4.042685444142945e-12, 5.650243773366653e-12, 7.896818537751913e-12, 1.1036307742174598e-11, 1.5423429614525036e-11, 2.1553726055994697e-11, 3.011942248045726e-11, 4.2087420741244583e-11, 5.880818211036204e-11, 8.216771538387709e-11, 1.147997054894844e-10, 1.603815352940665e-10, 2.240473115528605e-10, 3.1296403935229466e-10, 4.3713523517553623e-10, 6.105215229466906e-10, 8.52602890772976e-10, 1.1905561420504021e-09, 1.662288981010593e-09, 2.3206665097667656e-09, 3.2393968959134933e-09, 4.521224721498587e-09, 6.309332558781059e-09, 8.803200564079052e-09, 1.2280657457338146e-08, 1.7128525264058264e-08, 2.3885184894781535e-08, 3.329966647302377e-08, 4.641362948239142e-08, 6.467502413763038e-08, 9.009556384309048e-08, 1.2546872568777832e-07, 1.7467128911540467e-07, 2.430800425864799e-07, 3.3814707322843215e-07, 4.701931364465552e-07, 6.535005016880049e-07, 9.078164232026752e-07, 1.2604187070233036e-06, 1.7489493456900177e-06, 2.4252956412356184e-06, 3.36089691063394e-06, 4.6539869768874746e-06, 6.439458870011638e-06, 8.902272288078673e-06, 1.2295634090005293e-05, 1.696558992387263e-05, 2.3384199452644937e-05, 3.219416406447425e-05, 4.4268678480022345e-05, 6.079144030879221e-05, 8.336323995771415e-05, 0.00011414344625718829, 0.00015603709484323703, 0.00021294128829226007, 0.0002900683613606186, 0.00039436790880491144, 0.0005350755076954225, 0.0007244230284117436, 0.0009785541272720438, 0.001318699270333886, 0.0017726780564427257, 0.0023768135906518137, 0.0031783655947841905, 0.004238618001903086, 0.005636796391497631, 0.0074750462009749285, 0.00988478277324189, 0.013034842559373401, 0.017142042795247007, 0.02248502930216196, 0.029422714730332523, 0.03841927468618437, 0.05007873129396481, 0.06519387819817665, 0.08481715553524309, 0.11036591621066028, 0.143782922271076, 0.18778794020747866, 0.24628412498154922, 0.3250363950839906, 0.43284664499029174],
[1.9465833971606937e-14, 2.721320206743982e-14, 3.8043770865280345e-14, 5.31844300824469e-14, 7.435021788361202e-14, 1.0393850930758417e-13, 1.453004366071329e-13, 2.0312024883784352e-13, 2.839455225315713e-13, 3.969281879693305e-13, 5.548601610727672e-13, 7.756206572996943e-13, 1.0841987650350734e-12, 1.515519813631341e-12, 2.1183948042174783e-12, 2.961038897068618e-12, 4.13878192998629e-12, 5.784841083462266e-12, 8.08537088828589e-12, 1.1300487546733306e-11, 1.5793637075503825e-11, 2.2072615484349195e-11, 3.084685922905007e-11, 4.3107452111989395e-11, 6.023884496091452e-11, 8.417484148248917e-11, 1.1761636422072407e-10, 1.6433543076775418e-10, 2.295994109789688e-10, 3.20763070588133e-10, 4.48094623105721e-10, 6.259280787045893e-10, 8.742704703510725e-10, 1.2210430458933813e-09, 1.705205781545952e-09, 2.3811122841008042e-09, 3.324577962021186e-09, 4.641333019533531e-09, 6.478793791826987e-09, 9.042449442997174e-09, 1.2618665117562118e-08, 1.7606401128158104e-08, 2.4561314914676292e-08, 3.425705052811653e-08, 4.777036978956307e-08, 6.659933294604754e-08, 9.282725896478285e-08, 1.2935004827526077e-07, 1.8019112768618095e-07, 2.5093745137555663e-07, 3.4934257823080934e-07, 4.861600851729598e-07, 6.762941464568643e-07, 9.403862728931104e-07, 1.3070010033760099e-06, 1.8156328464053503e-06, 2.520837414046607e-06, 3.4978986913800353e-06, 4.850591282471237e-06, 6.72179382126788e-06, 9.307973953774949e-06, 1.2878917740023276e-05, 1.7804544576157346e-05, 2.4591268180010587e-05, 3.393117984774526e-05, 4.676839890528987e-05, 6.43883281289485e-05, 8.853735696004469e-05, 0.00012158288061758442, 0.0001667264799154283, 0.00022828689251437658, 0.00031207418968647407, 0.00042588257658452013, 0.0005801367227212372, 0.0007887358176098229, 0.001070151015390845, 0.0014488460568234873, 0.0019571082545440876, 0.002637398540667772, 0.0035453561128854514, 0.004753627181303627, 0.006356731189568381, 0.008477236003806171, 0.011273592782995261, 0.014950092401949857, 0.01976956554648378, 0.026069685118746803, 0.034284085590494014, 0.04497005860432392, 0.058845429460665045, 0.07683854937236874, 0.10015746258792962, 0.1303877563963533, 0.16963431107048618, 0.22073183242132055, 0.287565844542152, 0.3755758804149573, 0.49256824996309845, 0.6500727901679813, 0.8656932899805835],
[9.732916985803468e-15, 1.360660103371991e-14, 1.9021885432640173e-14, 2.659221504122345e-14, 3.717510894180601e-14, 5.1969254653792084e-14, 7.265021830356645e-14, 1.0156012441892176e-13, 1.4197276126578564e-13, 1.9846409398466525e-13, 2.774300805363836e-13, 3.8781032864984714e-13, 5.420993825175367e-13, 7.577599068156705e-13, 1.0591974021087391e-12, 1.480519448534309e-12, 2.069390964993145e-12, 2.892420541731133e-12, 4.042685444142945e-12, 5.650243773366653e-12, 7.896818537751913e-12, 1.1036307742174598e-11, 1.5423429614525036e-11, 2.1553726055994697e-11, 3.011942248045726e-11, 4.2087420741244583e-11, 5.880818211036204e-11, 8.216771538387709e-11, 1.147997054894844e-10, 1.603815352940665e-10, 2.240473115528605e-10, 3.1296403935229466e-10, 4.3713523517553623e-10, 6.105215229466906e-10, 8.52602890772976e-10, 1.1905561420504021e-09, 1.662288981010593e-09, 2.3206665097667656e-09, 3.2393968959134933e-09, 4.521224721498587e-09, 6.309332558781059e-09, 8.803200564079052e-09, 1.2280657457338146e-08, 1.7128525264058264e-08, 2.3885184894781535e-08, 3.329966647302377e-08, 4.641362948239142e-08, 6.467502413763038e-08, 9.009556384309048e-08, 1.2546872568777832e-07, 1.7467128911540467e-07, 2.430800425864799e-07, 3.3814707322843215e-07, 4.701931364465552e-07, 6.535005016880049e-07, 9.078164232026752e-07, 1.2604187070233036e-06, 1.7489493456900177e-06, 2.4252956412356184e-06, 3.36089691063394e-06, 4.6539869768874746e-06, 6.439458870011638e-06, 8.902272288078673e-06, 1.2295634090005293e-05, 1.696558992387263e-05, 2.3384199452644937e-05, 3.219416406447425e-05, 4.4268678480022345e-05, 6.079144030879221e-05, 8.336323995771415e-05, 0.00011414344625718829, 0.00015603709484323703, 0.00021294128829226007, 0.0002900683613606186, 0.00039436790880491144, 0.0005350755076954225, 0.0007244230284117436, 0.0009785541272720438, 0.001318699270333886, 0.0017726780564427257, 0.0023768135906518137, 0.0031783655947841905, 0.004238618001903086, 0.005636796391497631, 0.0074750462009749285, 0.00988478277324189, 0.013034842559373401, 0.017142042795247007, 0.02248502930216196, 0.029422714730332523, 0.03841927468618437, 0.05007873129396481, 0.06519387819817665, 0.08481715553524309, 0.11036591621066028, 0.143782922271076, 0.18778794020747866, 0.24628412498154922, 0.3250363950839906, 0.43284664499029174],
[-1.9988392978080736, -1.998737893140717, -1.9986276317794558, -1.9985077406388165, -1.998377379235719, -1.9982356338290062, -1.9980815110521668, -1.9979139309959255, -1.997731719693776, -1.9975336009596267, -1.997318187522544, -1.9970839713990447, -1.9968293134385406, -1.9965524319723098, -1.996251390490752, -1.9959240842676818, -1.9955682258439646, -1.9951813292759344, -1.994760693046662, -1.994303381530345, -1.9938062048917613, -1.9932656972939353, -1.9926780932778283, -1.9920393021680753, -1.9913448803484814, -1.990590001240214, -1.9897694228044465, -1.988877452379602, -1.987907908651479, -1.9868540805423769, -1.9857086827931494, -1.9844638079999066, -1.9831108748551474, -1.981640572331599, -1.9800427995363328, -1.9783066009530696, -1.9764200967824725, -1.9743704080841462, -1.9721435764205433, -1.9697244777028475, -1.9670967299428233, -1.9642425946237057, -1.9611428714184216, -1.957776786006141, -1.9541218707697043, -1.9501538381985697, -1.945846446876259, -1.941171359999911, -1.9360979964645697, -1.930593374648523, -1.9246219491607208, -1.918145440959398, -1.9111226614247914, -1.9035093311702274, -1.8952578946064904, -1.886317331534958, -1.876632967335261, -1.8661462836312603, -1.8547947316607782, -1.8425115509328305, -1.8292255961200745, -1.814861175488018, -1.7993379044839888, -1.782570578367965, -1.7644690679243815, -1.7449382422976956, -1.7238779227796102, -1.7011828708610397, -1.6767428129470638, -1.6504425026969634, -1.6221618198488208, -1.5917759014478683, -1.559155297419201, -1.5241661371763482, -1.4866702871681028, -1.4465254706244195, -1.4035853098995033, -1.3576992382818693, -1.308712211390317, -1.2564641275730277, -1.2007888410759435, -1.1415126197193337, -1.0784518583110496, -1.0114098068469604, -0.9401720038167095, -0.8645000120695375, -0.7841229258570664, -0.6987259341915358, -0.6079349578238639, -0.5112959770432993, -0.4082470566206675, -0.2980801213777357, -0.17988801678201824, -0.05248991003669645, 0.08567606276128167, 0.23671114505493918, 0.40349625074739637, 0.5900685358584165, 0.802233330594955, 1.0485995763626115],
[0.9988396923632011, 0.9987383596438452, 0.9986281833480194, 0.9985083927811003, 0.9983781502864275, 0.998236545464129, 0.9980825888975597, 0.9979152053466436, 0.9977332263642898, 0.997535382288698, 0.9973202935608517, 0.9970864613127411, 0.9968322571679225, 0.9965559121918812, 0.9962555049253249, 0.9959289484290306, 0.9955739762642, 0.9951881273274974, 0.9947687294550405, 0.9943128817047084, 0.993817435221218, 0.9932789725836373, 0.9926937855303831, 0.9920578509525073, 0.9913668050422784, 0.9906159154809334, 0.9898000515472655, 0.9889136520276155, 0.9879506908082926, 0.9869046400336968, 0.9857684307180864, 0.9845344107064175, 0.9831942998907253, 0.9817391426037908, 0.9801592571322976, 0.9784441823182588, 0.9765826212514035, 0.9745623820978254, 0.9723703161629502, 0.969992253351666, 0.9674129352670826, 0.9646159462842002, 0.9615836430480905, 0.9582970829807979, 0.9547359525398739, 0.9508784961574734, 0.946701447005413, 0.9421799609819322, 0.9372875556034023, 0.9319960558119869, 0.9262755490811113, 0.9200943526166017, 0.9134189959137595, 0.9062142224391786, 0.8984430147587907, 0.8900666480258257, 0.8810447773664062, 0.8713355653446574, 0.8608958563368816, 0.8496814052732995, 0.8376471687870424, 0.82474766730718, 0.8109374270012562, 0.7961715106607837, 0.7804061465706681, 0.7635994640450368, 0.7457123435789405, 0.7267093883912111, 0.706560022460586, 0.6852397179459497, 0.6627313521248992, 0.6390266907246008, 0.6141279908667062, 0.5880497130117452, 0.5608203276015039, 0.5324841990556992, 0.5031035280784387, 0.4727603338163895, 0.4415584615361012, 0.4096256107856713, 0.3771153955971516, 0.34420947494629756, 0.3111198321182167, 0.27809134092377225, 0.24540484215016947, 0.21338107604891157, 0.182385992854959, 0.1528382202154807, 0.12521984844988143, 0.10009227712597968, 0.078119780404543, 0.06010492706590599, 0.047042460733170595, 0.040202512009014764, 0.04126165231566124, 0.05251451686082635, 0.07722636177516791, 0.12024335878472586, 0.18909943257210599, 0.2961403575616695],
],
[
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[2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0],
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],
];
pub trait CutoffRatioBounds {
const MIN_CUTOFF_RATIO: f64;
const MAX_CUTOFF_RATIO: f64;
fn is_within_bounds(cutoff_ratio: f64) -> bool {
cutoff_ratio >= Self::MIN_CUTOFF_RATIO && cutoff_ratio <= Self::MAX_CUTOFF_RATIO
}
}
impl CutoffRatioBounds for f32 {
const MIN_CUTOFF_RATIO: f64 = MIN_CUTOFF_RATIO_F32;
const MAX_CUTOFF_RATIO: f64 = MAX_CUTOFF_RATIO_F32;
}
impl CutoffRatioBounds for f64 {
const MIN_CUTOFF_RATIO: f64 = MIN_CUTOFF_RATIO_F64;
const MAX_CUTOFF_RATIO: f64 = MAX_CUTOFF_RATIO_F64;
}
/// Butterworth order 4 lowpass filter, second order sections (SOS) implementation.
/// The filter is created by interpolating the SOS coefficients from stored tables.
///
/// `cutoff_ratio` (dimensionless) is the cutoff frequency divided by the sample frequency.
///
/// Region of validity for `cutoff_ratio` depends on the float type `T`:
/// * f32: 0.0050 to 0.4000
/// * f64: 0.0005 to 0.4000
pub fn butter4<T>(cutoff_ratio: f64) -> Result<SisoSosFilter<NUM_SECTIONS, T>, &'static str>
where
T: Num
+ Copy
+ MulAdd<Output = T>
+ Neg<Output = T>
+ FromPrimitive
+ ToPrimitive
+ CutoffRatioBounds,
{
if !T::is_within_bounds(cutoff_ratio) {
return Err("cutoff_ratio out of bounds for provided float type");
}
// Convert SOS tables from static arrays to slices because new_interpolated expects slices.
let sos_tables = SOS_TABLES
.each_ref()
.map(|sec| sec.each_ref().map(|coeffs| &coeffs[..]));
SisoSosFilter::new_interpolated(cutoff_ratio, &LOG10_CUTOFF_RATIOS, sos_tables)
}
#[cfg(test)]
mod tests {
use super::super::super::test_helpers::test_filter;
use super::{
MAX_CUTOFF_RATIO_F32, MAX_CUTOFF_RATIO_F64, MIN_CUTOFF_RATIO_F32, MIN_CUTOFF_RATIO_F64,
NUM_SECTIONS, butter4,
};
#[test]
fn test_butter4_f32() {
test_filter::<NUM_SECTIONS, f32>(MIN_CUTOFF_RATIO_F32, MAX_CUTOFF_RATIO_F32, butter4);
}
#[test]
fn test_butter4_f64() {
test_filter::<NUM_SECTIONS, f64>(MIN_CUTOFF_RATIO_F64, MAX_CUTOFF_RATIO_F64, butter4);
}
}