First of all, please forgive my direct and simple language and the fact that I’m oversimplifying things here, it’s not easy for me to write about technical stuff. If anyone disagrees with certain things, they’re welcome to correct me.
When I realized that a new Resample UGen would be included in the development of SC 3.15, I thought it would be nice if we also had good anti-aliasing filters. The example in the 3.15 documentation uses two LPFs as an example before downsampling. However, LPFs aren’t really suitable for this purpose. Other filters in SC are also unsuitable for this purpose because they cannot roll off sharply in the middle of the frequency band while maintaining a stopband. That’s what FIR filters are for.
The reason for this is that LPFs behave differently in the resample-graph at higher sampling rates. At a sampling rate of 48000 and a cutoff frequency of 21 kHz, a 2x LPF yields the following attenuation values (rounded):
15KHz: -0.1dB, 18kHz: -0.5dB, 20kHz: -2.3dB, 21kHz: -6dB,
22kHz: -16dB, 23kHz: -39dB, 23.9kHz -118dB
However, this does not apply at a sampling rate of 96000 or when using “Resample(2)” with a cutoff frequency of 21 kHz and 2x LPF (rounded):
15KHz: -1.4dB, 18kHz: -3.1dB, 20kHz: -5dB, 21kHz: -6dB,
22kHz: -7.3dB, 23kHz: -9dB, 24kHz -11dB, 30kHz: -22dB > very bad AA-effect here!
This means: If you use 2x an LPF with “Resample(2)” before downsampling to filter out frequencies (AA components) above the target nyquist frequency, you’ll end up with a very flat filter with an attenuation of only -10 dB at 24kHz, as well as a very poor frequency response in the passband, an area that an AA filter shouldn’t actually affect.
For this reason, I decided to create some FIR AA filters for the community in advance. These FIR kernels are loaded as buffers using the Convolution2 UGen, and it’s very important that you use the correct kernel depending on the resample rate you’re using.
For now, I have created three FIR filters, all of which have the same specifications:
- The target downsampling rate is always 48000.
- Passband up to 20.5 kHz, deviation less than 0.005 dB, which essentially means no impact on lower frequencies.
- Transitionband up to 24 kHz: 21 kHz: -0.4dB, 21.5 kHz: -2dB, 22 kHz: -6dB, 22.5 kHz: -13dB, 23 kHz: -25dB, 23.5 kHz: -44dB, 24 kHz: -95dB
- Rejection band: at least -95dB at and above 24 kHz
The size of the filter varies depending on the oversampling rate:
- 96k: 128 Samples (Resample 2x)
- 192k: 256 Samples (Resample 4x)
- 384k: 512 Samples (Resample 8x)
Since Convolution2’s CPU usage depends on the frame size and must be a power of two, I also used a power of two to maximize the filter specifications while minimizing CPU usage.
If anyone wants a different filter specification, it’s easy to create another one. Since I don’t have the development version of SC 3.15, I can only test it by changing the sampling rate in scsynth. Could someone please test my filters with 3.15 and Resample UGen?
You can also test these kernels by setting the sampling rate of the scsynth server to 96000 or higher!
Here are the kernels, instructions for using them with 3.14.1, and an example that should work for 3.15.
// IF you don't use the Resample(2) UGen in 3.15-dev: set serveroption for sample rate to 96k
s.options.sampleRate = 96000;
// boot server
s.boot;
// post the servers actual sample rate
s.actualSampleRate.round(1).postln;
// load the FIR kernel for sample rate 96k / 48k with Resample(2)
(
~kernelFir48k_2x_95dB_128S = Buffer.loadCollection(s, [
3.10735094911491e-05, 9.87601637951595e-06, -1.10737477267071e-04, -2.11815991000221e-04,
-9.76883186992134e-05, 1.41279669797449e-04, 1.39206575249781e-04, -1.57955220091580e-04,
-2.56626749949320e-04, 1.16778781660566e-04, 3.88510701097779e-04, -1.66845850300382e-05,
-5.21693094574120e-04, -1.59792042395175e-04, 6.25775870931313e-04, 4.17846946742348e-04,
-6.64916289573010e-04, -7.51202292541550e-04, 5.98997430351011e-04, 1.13802978771451e-03,
-3.88777755734192e-04, -1.53906230018351e-03, 2.05560715942015e-06, 1.89748942715106e-03,
5.79300972416281e-04, -2.14128997234175e-03, -1.35230882133037e-03, 2.18820215685515e-03,
2.28671057711517e-03, -1.95324604628126e-03, -3.32063289300062e-03, 1.35837213021172e-03,
4.35889104822858e-03, -3.43483218672593e-04, -5.27452605522543e-03, -1.12217600177471e-03,
5.91379851894811e-03, 3.02940358657481e-03, -6.10439807785135e-03, -5.32030829203232e-03,
5.66609305472552e-03, 7.88232869743182e-03, -4.42246088869304e-03, -1.05453716477607e-02,
2.21168886094490e-03, 1.30815899590126e-02, 1.10639419349884e-03, -1.52059139806634e-02,
-5.65127539382519e-03, 1.65728896168359e-02, 1.15378913380359e-02, -1.67599472520647e-02,
-1.89227860838246e-02, 1.52134569134602e-02, 2.81177787108968e-02, -1.10920286575042e-02,
-3.98866339561082e-02, 2.78452499627548e-03, 5.63754114108983e-02, 1.39042568242949e-02,
-8.51893225082190e-02, -5.63410254947792e-02, 1.75944051284943e-01, 4.19926559238836e-01,
4.19926559238836e-01, 1.75944051284943e-01, -5.63410254947792e-02, -8.51893225082190e-02,
1.39042568242949e-02, 5.63754114108983e-02, 2.78452499627548e-03, -3.98866339561082e-02,
-1.10920286575042e-02, 2.81177787108968e-02, 1.52134569134602e-02, -1.89227860838246e-02,
-1.67599472520647e-02, 1.15378913380359e-02, 1.65728896168359e-02, -5.65127539382519e-03,
-1.52059139806634e-02, 1.10639419349884e-03, 1.30815899590126e-02, 2.21168886094490e-03,
-1.05453716477607e-02, -4.42246088869304e-03, 7.88232869743182e-03, 5.66609305472552e-03,
-5.32030829203232e-03, -6.10439807785135e-03, 3.02940358657481e-03, 5.91379851894811e-03,
-1.12217600177471e-03, -5.27452605522543e-03, -3.43483218672593e-04, 4.35889104822858e-03,
1.35837213021172e-03, -3.32063289300062e-03, -1.95324604628126e-03, 2.28671057711517e-03,
2.18820215685515e-03, -1.35230882133037e-03, -2.14128997234175e-03, 5.79300972416281e-04,
1.89748942715106e-03, 2.05560715942015e-06, -1.53906230018351e-03, -3.88777755734192e-04,
1.13802978771451e-03, 5.98997430351011e-04, -7.51202292541550e-04, -6.64916289573010e-04,
4.17846946742348e-04, 6.25775870931313e-04, -1.59792042395175e-04, -5.21693094574120e-04,
-1.66845850300382e-05, 3.88510701097779e-04, 1.16778781660566e-04, -2.56626749949320e-04,
-1.57955220091580e-04, 1.39206575249781e-04, 1.41279669797449e-04, -9.76883186992134e-05,
-2.11815991000221e-04, -1.10737477267071e-04, 9.87601637951595e-06, 3.10735094911491e-05
]);
)
// post kernel size
~kernelFir48k_2x_95dB_128S.numFrames;
// plot kernel if you like to see
~kernelFir48k_2x_95dB_128S.plot;
// using the kernel in a SynthDef without Resample, but with server sample rate 96k for testing
// adjust the size in Convolution2 according to the kernel size
(
SynthDef(\filter01, {
arg out=0, amp=0.2, kernel=0;
var sig;
sig = WhiteNoise.ar(amp) ! 2;
sig = Convolution2.ar(sig, kernel, 0, 128);
Out.ar(out, sig);
}).add;
)
// using the kernel in a SynthDef with Resample:
(
SynthDef(\filter01, {
arg out=0, amp=0.2, kernel=0;
var sig;
Resample(2);
sig = WhiteNoise.ar(amp) ! 2;
sig = Convolution2.ar(sig, kernel, 0, 128);
Out.ar(out, sig);
}).add;
)
~filter01 = Synth(\filter01, [amp: 0.2, kernel: ~kernelFir48k_2x_95dB_128S]);
~filter01.free;
// FIR kernel for sample rate 192k / 48k with Resample(4)
~kernelFir48k_4x_95dB_256S = Buffer.loadCollection(s, [
1.70723691932502e-05, 1.80792387492879e-05, 1.43231981011602e-05, -3.61170983610532e-06,
-3.52737209750031e-05, -7.24633025066862e-05, -1.00642118305463e-04, -1.04500091123357e-04,
-7.58226933524237e-05, -1.98865110612319e-05, 4.36281825886469e-05, 8.71951694851486e-05,
8.77709108396947e-05, 3.95639566808192e-05, -3.95696764461494e-05, -1.12928904359150e-04,
-1.40687088920571e-04, -1.00234509626169e-04, -1.09522869952055e-06, 1.14595833878083e-04,
1.88904165587220e-04, 1.76194917166450e-04, 6.93686837728316e-05, -9.01514026687766e-05,
-2.26694558123647e-04, -2.65122004093280e-04, -1.70716512686001e-04, 2.63668515290303e-05,
2.37493700786023e-04, 3.53958641079463e-04, 3.01593692454309e-04, 8.47948375120163e-05,
-2.04970572553852e-04, -4.25626212792693e-04, -4.52667010572400e-04, -2.47097824102674e-04,
1.12958592361456e-04, 4.58468693350772e-04, 6.07024795941677e-04, 4.57129640976647e-04,
5.14246853887339e-05, -4.28371069900572e-04, -7.40384034284019e-04, -7.02497680205414e-04,
-2.94800637387069e-04, 3.11470680202063e-04, 8.22154472888615e-04, 9.60598088076277e-04,
6.14449751322455e-04, -8.76992993612036e-05, -8.17742494277761e-04, -1.19848609083670e-03,
-9.95677600571714e-04, -2.55233797083610e-04, 6.91999964230900e-04, 1.37406637055806e-03,
1.41004110175467e-03, 7.17821810164684e-04, -4.13626025371020e-04, -1.43872602787745e-03,
-1.81482595170527e-03, -1.28518677010350e-03, -3.98279507854403e-05, 1.34136395562689e-03,
2.15406349546994e-03, 1.92444796842065e-03, 6.76826344583535e-04, -1.03358199499595e-03,
-2.36120774355083e-03, -2.58345935026493e-03, -1.48713032824841e-03, 4.75633874044843e-04,
2.36339371654037e-03, 3.19120488601552e-03, 2.43802394441601e-03, 3.57406914567850e-04,
-2.08697664630256e-03, -3.65993189909953e-03, -3.47192353784879e-03, -1.46987527402549e-03,
1.46382285599018e-03, 3.88881705061292e-03, 4.50559839390012e-03, 2.84073215724165e-03,
-4.37624868839988e-04, -3.76861499157747e-03, -5.43090409233912e-03, -4.42023735348557e-03,
-1.03066512423811e-03, 3.18629923791483e-03, 6.11642953486911e-03, 6.12826884710284e-03,
2.95936244711559e-03, -2.02807980667308e-03, -6.40866347856084e-03, -7.85399395446830e-03,
-5.34587179032258e-03, 1.78106401281226e-04, 6.12985595407493e-03, 9.45572617713220e-03,
8.17173292202695e-03, 2.49213199371040e-03, -5.06669365724040e-03, -1.07580238201416e-02,
-1.14164985541796e-02, -6.15454447503820e-03, 2.93613383234335e-03, 1.15386890871853e-02,
1.50892031030841e-02, 1.11034027212976e-02, 7.08669968736540e-04, -1.14849690771299e-02,
-1.93039370921887e-02, -1.79710628406303e-02, -6.75507928085145e-03, 1.00471285629608e-02,
2.45003368843427e-02, 2.84374242862899e-02, 1.75235039662254e-02, -5.85054457664745e-03,
-3.23421109995325e-02, -4.85469659623459e-02, -4.21070420453171e-02, -7.07528891932349e-03,
5.27081256316807e-02, 1.23807431380313e-01, 1.87148066685396e-01, 2.24399189900108e-01,
2.24399189900108e-01, 1.87148066685396e-01, 1.23807431380313e-01, 5.27081256316807e-02,
-7.07528891932349e-03, -4.21070420453171e-02, -4.85469659623459e-02, -3.23421109995325e-02,
-5.85054457664745e-03, 1.75235039662254e-02, 2.84374242862899e-02, 2.45003368843427e-02,
1.00471285629608e-02, -6.75507928085145e-03, -1.79710628406303e-02, -1.93039370921887e-02,
-1.14849690771299e-02, 7.08669968736540e-04, 1.11034027212976e-02, 1.50892031030841e-02,
1.15386890871853e-02, 2.93613383234335e-03, -6.15454447503820e-03, -1.14164985541796e-02,
-1.07580238201416e-02, -5.06669365724040e-03, 2.49213199371040e-03, 8.17173292202695e-03,
9.45572617713220e-03, 6.12985595407493e-03, 1.78106401281226e-04, -5.34587179032258e-03,
-7.85399395446830e-03, -6.40866347856084e-03, -2.02807980667308e-03, 2.95936244711559e-03,
6.12826884710284e-03, 6.11642953486911e-03, 3.18629923791483e-03, -1.03066512423811e-03,
-4.42023735348557e-03, -5.43090409233912e-03, -3.76861499157747e-03, -4.37624868839988e-04,
2.84073215724165e-03, 4.50559839390012e-03, 3.88881705061292e-03, 1.46382285599018e-03,
-1.46987527402549e-03, -3.47192353784879e-03, -3.65993189909953e-03, -2.08697664630256e-03,
3.57406914567850e-04, 2.43802394441601e-03, 3.19120488601552e-03, 2.36339371654037e-03,
4.75633874044843e-04, -1.48713032824841e-03, -2.58345935026493e-03, -2.36120774355083e-03,
-1.03358199499595e-03, 6.76826344583535e-04, 1.92444796842065e-03, 2.15406349546994e-03,
1.34136395562689e-03, -3.98279507854403e-05, -1.28518677010350e-03, -1.81482595170527e-03,
-1.43872602787745e-03, -4.13626025371020e-04, 7.17821810164684e-04, 1.41004110175467e-03,
1.37406637055806e-03, 6.91999964230900e-04, -2.55233797083610e-04, -9.95677600571714e-04,
-1.19848609083670e-03, -8.17742494277761e-04, -8.76992993612036e-05, 6.14449751322455e-04,
9.60598088076277e-04, 8.22154472888615e-04, 3.11470680202063e-04, -2.94800637387069e-04,
-7.02497680205414e-04, -7.40384034284019e-04, -4.28371069900572e-04, 5.14246853887339e-05,
4.57129640976647e-04, 6.07024795941677e-04, 4.58468693350772e-04, 1.12958592361456e-04,
-2.47097824102674e-04, -4.52667010572400e-04, -4.25626212792693e-04, -2.04970572553852e-04,
8.47948375120163e-05, 3.01593692454309e-04, 3.53958641079463e-04, 2.37493700786023e-04,
2.63668515290303e-05, -1.70716512686001e-04, -2.65122004093280e-04, -2.26694558123647e-04,
-9.01514026687766e-05, 6.93686837728316e-05, 1.76194917166450e-04, 1.88904165587220e-04,
1.14595833878083e-04, -1.09522869952055e-06, -1.00234509626169e-04, -1.40687088920571e-04,
-1.12928904359150e-04, -3.95696764461494e-05, 3.95639566808192e-05, 8.77709108396947e-05,
8.71951694851486e-05, 4.36281825886469e-05, -1.98865110612319e-05, -7.58226933524237e-05,
-1.04500091123357e-04, -1.00642118305463e-04, -7.24633025066862e-05, -3.52737209750031e-05,
-3.61170983610532e-06, 1.43231981011602e-05, 1.80792387492879e-05, 1.70723691932502e-05
]);
)
// FIR kernel for sample rate 384k / 48k with Resample(8)
~kernelFir48k_8x_95dB_512S = Buffer.loadCollection(s, [
1.23064223528150e-05, 8.56209390195851e-06, 1.02135118329274e-05, 1.08953123650380e-05,
1.01681101766024e-05, 7.67319123495313e-06, 3.20221056363857e-06, -3.24140880445665e-06,
-1.13998867506142e-05, -2.07467150023188e-05, -3.05072426041582e-05, -3.97168951888198e-05,
-4.73146752026809e-05, -5.22641958813905e-05, -5.36894924209287e-05, -5.10090073723377e-05,
-4.40491729387362e-05, -3.31194226681453e-05, -1.90334988749114e-05, -3.06745652476350e-06,
1.31476913642627e-05, 2.77920265363555e-05, 3.90660206946632e-05, 4.54199808697347e-05,
4.57752592204873e-05, 3.97068939072248e-05, 2.75593642429868e-05, 1.04732590597708e-05,
-9.68956200627949e-06, -3.05222680475741e-05, -4.93370888467211e-05, -6.34902158761089e-05,
-7.07299936219836e-05, -6.95242033733937e-05, -5.93208523216142e-05, -4.07021705585527e-05,
-1.54016801658050e-05, 1.38294639916733e-05, 4.35019446787506e-05, 6.97884852709189e-05,
8.90014238009475e-05, 9.80902938141359e-05, 9.50946528633114e-05, 7.94881525617226e-05,
5.23593081015779e-05, 1.63920144701768e-05, -2.43671725190895e-05, -6.49403692384107e-05,
-1.00005924622649e-04, -1.24575638661258e-04, -1.34678023441314e-04, -1.27956930864333e-04,
-1.04099491676875e-04, -6.50238647254600e-05, -1.47844122448662e-05, 4.08132916336977e-05,
9.48569000994849e-05, 1.40163567480821e-04, 1.70210036486759e-04, 1.80039159392104e-04,
1.67020518332613e-04, 1.31353919933643e-04, 7.62313641532546e-05, 7.61310816929172e-06,
-6.63779152108550e-05, -1.36387983001117e-04, -1.92988367957606e-04, -2.27915056011294e-04,
-2.35233993550712e-04, -2.12271252017667e-04, -1.60170155032066e-04, -8.39775952950108e-05,
7.78122360377424e-06, 1.04014839010630e-04, 1.92373157779393e-04, 2.60801147011568e-04,
2.99147190392864e-04, 3.00615860572138e-04, 2.62862960774309e-04, 1.88566262108239e-04,
8.53652952938496e-05, -3.48587560935866e-05, -1.57305904381623e-04, -2.66042309104148e-04,
-3.46037135637394e-04, -3.85195606791837e-04, -3.76118502192900e-04, -3.17339489618236e-04,
-2.13847114227487e-04, -7.67825424606883e-05, 7.76923933695118e-05, 2.30252422952224e-04,
3.60784894169767e-04, 4.50998100905384e-04, 4.86929016206925e-04, 4.61013063206983e-04,
3.73418651507729e-04, 2.32430904431204e-04, 5.37837800597749e-05, -1.41025917518185e-04,
-3.27272763826035e-04, -4.80093570309401e-04, -5.77754896757122e-04, -6.04674051045085e-04,
-5.53781653132284e-04, -4.27880108607079e-04, -2.39767913890716e-04, -1.10516039918826e-05,
2.30262988891094e-04, 4.53142351577243e-04, 6.27461792054856e-04, 7.28014530565822e-04,
7.38067420257889e-04, 6.51971733916228e-04, 4.76438659131244e-04, 2.30246935055086e-04,
-5.76537644621427e-05, -3.51469739877918e-04, -6.12949183260898e-04, -8.06298316893486e-04,
-9.03004037542826e-04, -8.85922507435768e-04, -7.52060249980685e-04, -5.13620392019486e-04,
-1.97096059156508e-04, 1.59559242303208e-04, 5.11399190717482e-04, 8.12075905155750e-04,
1.01986896950631e-03, 1.10337749287827e-03, 1.04611005260341e-03, 8.49318415837528e-04,
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]);
)
And here you can see a graph showing how two LPFs behave at a 96k sample rate with a cutoff of 21kHz, followed by my filter, and then my three FIR filter plots.
