{"inputs":{"type":"lowpass","freqHz":1000,"fs":48000,"q":0.7071067811865476,"gainDb":0},"result":{"groupDelayMs":0.22572310603430518,"type":{"slug":"lowpass","label":"Low-pass","noun":"low-pass filter","defaultQ":0.7071067811865476,"defaultGainDb":0,"usesGain":false,"f0Db":-3.0103,"purpose":"Passes everything below the corner and rolls off above it at 12 dB/octave."},"freqHz":1000,"fs":48000,"q":0.7071067811865476,"gainDb":0,"coeffs":{"b0":0.003916126660547383,"b1":0.007832253321094766,"b2":0.003916126660547383,"a0":1,"a1":-1.815341082704568,"a2":0.8310055893467576},"poles":{"real":false,"radii":[0.9115950797074092,0.9115950797074092],"maxRadius":0.9115950797074092,"theta":0.09282484477211987},"zeros":{"real":true,"radii":[1,1],"maxRadius":1,"theta":null},"dcDb":-4.821637332766449e-14,"f0Db":-3.010299956639777,"nyquistDb":-334.7433394195403,"peakDb":-4.318207296603919e-8,"peakAtHz":10,"minus3LowHz":null,"minus3HighHz":1000.0000099351195,"rates":[{"fs":8000,"coeffs":{"b0":0.09763107293781748,"b1":0.19526214587563495,"b2":0.09763107293781748,"a0":1,"a1":-0.9428090415820635,"a2":0.3333333333333333},"poles":{"real":false,"radii":[0.5773502691896257,0.5773502691896257],"maxRadius":0.5773502691896257,"theta":0.6154797086703871},"nyquistFraction":0.25,"f0Db":-3.0102999566398116},{"fs":16000,"coeffs":{"b0":0.029954582208092478,"b1":0.059909164416184955,"b2":0.029954582208092478,"a0":1,"a1":-1.4542435862515848,"a2":0.5740619150839548},"poles":{"real":false,"radii":[0.75766873703747,0.75766873703747],"maxRadius":0.75766873703747,"theta":0.2849241266220628},"nyquistFraction":0.125,"f0Db":-3.0102999566398116},{"fs":22050,"coeffs":{"b0":0.01681915010705712,"b1":0.03363830021411424,"b2":0.01681915010705712,"a0":1,"a1":-1.601092394183619,"a2":0.6683689946118475},"poles":{"real":false,"radii":[0.8175383750086889,0.8175383750086889],"maxRadius":0.8175383750086889,"theta":0.20423988099258802},"nyquistFraction":0.09070294784580499,"f0Db":-3.010299956639815},{"fs":32000,"coeffs":{"b0":0.008442692929079959,"b1":0.016885385858159917,"b2":0.008442692929079959,"a0":1,"a1":-1.7237761727625094,"a2":0.7575469444788291},"poles":{"real":false,"radii":[0.8703717277570711,0.8703717277570711],"maxRadius":0.8703717277570711,"theta":0.1397356289388815},"nyquistFraction":0.0625,"f0Db":-3.010299956639792},{"fs":44100,"coeffs":{"b0":0.004603998475022464,"b1":0.009207996950044928,"b2":0.004603998475022464,"a0":1,"a1":-1.799096409484668,"a2":0.817512403384758},"poles":{"real":false,"radii":[0.9041639250626835,0.9041639250626835],"maxRadius":0.9041639250626835,"theta":0.10108717990213778},"nyquistFraction":0.045351473922902494,"f0Db":-3.0102999566398116},{"fs":48000,"coeffs":{"b0":0.003916126660547383,"b1":0.007832253321094766,"b2":0.003916126660547383,"a0":1,"a1":-1.815341082704568,"a2":0.8310055893467576},"poles":{"real":false,"radii":[0.9115950797074092,0.9115950797074092],"maxRadius":0.9115950797074092,"theta":0.09282484477211987},"nyquistFraction":0.041666666666666664,"f0Db":-3.010299956639777},{"fs":96000,"coeffs":{"b0":0.0010232176384709138,"b1":0.0020464352769418276,"b2":0.0010232176384709138,"a0":1,"a1":-1.9075016260460762,"a2":0.91159449659996},"poles":{"real":false,"radii":[0.9547745789451875,0.9547745789451875],"maxRadius":0.9547745789451875,"theta":0.04631308624221879},"nyquistFraction":0.020833333333333332,"f0Db":-3.010299956639723},{"fs":192000,"coeffs":{"b0":0.00026165269506587055,"b1":0.0005233053901317411,"b2":0.00026165269506587055,"a0":1,"a1":-1.9537279491407762,"a2":0.9547745599210397},"poles":{"real":false,"radii":[0.9771256622978641,0.9771256622978641],"maxRadius":0.9771256622978641,"theta":0.023144145931710335},"nyquistFraction":0.010416666666666666,"f0Db":-3.0102999566404565}],"words":[{"key":"float64","label":"float64","coeffs":{"b0":0.003916126660547383,"b1":0.007832253321094766,"b2":0.003916126660547383,"a0":1,"a1":-1.815341082704568,"a2":0.8310055893467576},"qFormat":null,"poles":{"real":false,"radii":[0.9115950797074092,0.9115950797074092],"maxRadius":0.9115950797074092,"theta":0.09282484477211987},"stable":true,"worstErrorDb":null,"worstErrorAtHz":null},{"key":"float32","label":"float32","coeffs":{"b0":0.003916126675903797,"b1":0.007832253351807594,"b2":0.003916126675903797,"a0":1,"a1":-1.8153411149978638,"a2":0.8310055732727051},"qFormat":null,"poles":{"real":false,"radii":[0.9115950708909658,0.9115950708909658],"maxRadius":0.9115950708909658,"theta":0.09282454978987786},"stable":true,"worstErrorDb":0.000026850716045393597,"worstErrorAtHz":10},{"key":"fixed32","label":"32-bit fixed","coeffs":{"b0":0.003916126675903797,"b1":0.007832253351807594,"b2":0.003916126675903797,"a0":1,"a1":-1.8153410824015737,"a2":0.8310055891051888},"qFormat":{"intBits":1,"fracBits":30},"poles":{"real":false,"radii":[0.9115950795749113,0.9115950795749113],"maxRadius":0.9115950795749113,"theta":0.09282484500372117},"stable":true,"worstErrorDb":3.5796645647678815e-8,"worstErrorAtHz":2985.72684120468},{"key":"fixed24","label":"24-bit fixed","coeffs":{"b0":0.003916025161743164,"b1":0.00783228874206543,"b2":0.003916025161743164,"a0":1,"a1":-1.8153409957885742,"a2":0.8310055732727051},"qFormat":{"intBits":1,"fracBits":22},"poles":{"real":false,"radii":[0.9115950708909658,0.9115950708909658],"maxRadius":0.9115950708909658,"theta":0.09282525519318896},"stable":true,"worstErrorDb":0.00013219851855428676,"worstErrorAtHz":10},{"key":"fixed16","label":"16-bit fixed","coeffs":{"b0":0.00390625,"b1":0.0078125,"b2":0.00390625,"a0":1,"a1":-1.81536865234375,"a2":0.83099365234375},"qFormat":{"intBits":1,"fracBits":14},"poles":{"real":false,"radii":[0.9115885323673999,0.9115885323673999],"maxRadius":0.9115885323673999,"theta":0.09258424046934609},"stable":true,"worstErrorDb":0.02692806587736385,"worstErrorAtHz":1506.759934915174}],"qSweep":[{"value":0.5,"coeffs":{"b0":0.0037836976644431432,"b1":0.0075673953288862865,"b2":0.0037836976644431432,"a0":1,"a1":-1.7539529259855138,"a2":0.7690877166432862},"f0Db":-6.020599913279589,"peakDb":-0.0008660665892234256,"peakAtHz":10,"minus3Hz":644.2424436003173,"maxRadius":0.8769764735294691,"groupDelayMs":0.15961039245583242},{"value":0.7071067811865476,"coeffs":{"b0":0.003916126660547383,"b1":0.007832253321094766,"b2":0.003916126660547383,"a0":1,"a1":-1.815341082704568,"a2":0.8310055893467576},"f0Db":-3.010299956639777,"peakDb":-4.318207296603919e-8,"peakAtHz":10,"minus3Hz":1000.0000099351195,"maxRadius":0.9115950797074092,"groupDelayMs":0.22572310603430518},{"value":1,"coeffs":{"b0":0.004015505022857752,"b1":0.008031010045715504,"b2":0.004015505022857752,"a0":1,"a1":-1.8614084445321082,"a2":0.8774704646235392},"f0Db":2.314385919727886e-14,"peakDb":1.2491145127745193,"peakAtHz":712.4456981320011,"minus3Hz":1168.1843147423306,"maxRadius":0.9367339348094202,"groupDelayMs":0.3192204638615984},{"value":2,"coeffs":{"b0":0.00414239650255865,"b1":0.0082847930051173,"b2":0.00414239650255865,"a0":1,"a1":-1.920229656436938,"a2":0.9367992424471726},"f0Db":6.020599913279687,"peakDb":6.292958786014533,"peakAtHz":924.4787110161315,"minus3Hz":1165.5948454024074,"maxRadius":0.9678838992602226,"groupDelayMs":0.6384383593481985},{"value":4,"coeffs":{"b0":0.0042088978862774564,"b1":0.008417795772554913,"b2":0.0042088978862774564,"a0":1,"a1":-1.951056722154107,"a2":0.9678923136992169},"f0Db":12.041199826559357,"peakDb":12.108005279832819,"peakAtHz":986.6956218842213,"minus3Hz":1102.7816733124848,"maxRadius":0.983815182693994,"groupDelayMs":1.2768561724241385},{"value":10,"coeffs":{"b0":0.00424983358333473,"b1":0.00849966716666946,"b2":0.00424983358333473,"a0":1,"a1":-1.970032679537168,"a2":0.9870320138705071},"f0Db":19.999999999999932,"peakDb":19.8140428580633,"peakAtHz":986.6956218842213,"minus3Hz":1048.3754886986578,"maxRadius":0.9934948484368236,"groupDelayMs":3.191780954618915}],"gainSweep":[]},"provenance":{"method":"RBJ Audio EQ Cookbook coefficients solved in float64, with pole and zero radii from the quadratic roots (never from sqrt(|a2|)), the response curve, the real −3 dB crossings, and what 16/24/32-bit word lengths do to stability and in-band error. Pure mathematics — nothing is fetched and nothing is recalled.","canonicalUrl":"https://makerportal.ai/lab/biquad/lowpass/1000-hz"},"license":"free-with-attribution"}