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Optimized compute of distance filters using log-quantized lookup tables.
Magnitude error < 0.25dB for entire parameter space.
This commit is contained in:
Ken Cooke
parent
7a4bdc1779
commit
fa55fc84f5
1 changed files with 159 additions and 94 deletions
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@ -16,6 +16,13 @@
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#include "AudioHRTF.h"
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#include "AudioHRTFData.h"
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#ifndef MAX
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#define MAX(a,b) (((a) > (b)) ? (a) : (b))
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#endif
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#ifndef MIN
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#define MIN(a,b) (((a) < (b)) ? (a) : (b))
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#endif
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//
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// Equal-gain crossfade
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//
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@ -58,6 +65,103 @@ static const float crossfadeTable[HRTF_BLOCK] = {
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0.0024846123f, 0.0019026510f, 0.0013981014f, 0.0009710421f, 0.0006215394f, 0.0003496476f, 0.0001554090f, 0.0000388538f,
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};
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//
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// Model the frequency-dependent attenuation of sound propogation in air.
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//
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// Fit using linear regression to a log-log model of lowpass cutoff frequency vs distance,
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// loosely based on data from Handbook of Acoustics. Only the onset of significant
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// attenuation is modelled, not the filter slope.
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//
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// 1m -> -3dB @ 55kHz
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// 10m -> -3dB @ 12kHz
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// 100m -> -3dB @ 2.5kHz
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// 1km -> -3dB @ 0.6kHz
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// 10km -> -3dB @ 0.1kHz
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//
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static const int NLOWPASS = 64;
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static const float lowpassTable[NLOWPASS][5] = { // { b0, b1, b2, a1, a2 }
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// distance = 1
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{ 0.999772371f, 1.399489756f, 0.454495527f, 1.399458985f, 0.454298669f },
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{ 0.999631480f, 1.357609808f, 0.425210203f, 1.357549905f, 0.424901586f },
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{ 0.999405154f, 1.311503050f, 0.394349994f, 1.311386830f, 0.393871368f },
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{ 0.999042876f, 1.260674595f, 0.361869089f, 1.260450057f, 0.361136504f },
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// distance = 2
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{ 0.998465222f, 1.204646525f, 0.327757118f, 1.204214978f, 0.326653886f },
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{ 0.997548106f, 1.143019308f, 0.292064663f, 1.142195387f, 0.290436690f },
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{ 0.996099269f, 1.075569152f, 0.254941286f, 1.074009405f, 0.252600301f },
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{ 0.993824292f, 1.002389610f, 0.216688640f, 0.999469185f, 0.213433357f },
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// distance = 4
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{ 0.990280170f, 0.924075266f, 0.177827150f, 0.918684864f, 0.173497723f },
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{ 0.984818279f, 0.841917936f, 0.139164195f, 0.832151968f, 0.133748443f },
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{ 0.976528670f, 0.758036513f, 0.101832398f, 0.740761682f, 0.095635899f },
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{ 0.964216485f, 0.675305244f, 0.067243474f, 0.645654855f, 0.061110348f },
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// distance = 8
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{ 0.946463038f, 0.596943020f, 0.036899688f, 0.547879974f, 0.032425772f },
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{ 0.921823868f, 0.525770189f, 0.012060451f, 0.447952111f, 0.011702396f },
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{ 0.890470015f, 0.463334299f, -0.001227816f, 0.347276405f, 0.005300092f },
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{ 0.851335343f, 0.407521164f, -0.009353968f, 0.241900234f, 0.007602305f },
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// distance = 16
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{ 0.804237360f, 0.358139558f, -0.014293332f, 0.130934213f, 0.017149373f },
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{ 0.750073259f, 0.314581568f, -0.016625381f, 0.014505388f, 0.033524057f },
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{ 0.690412072f, 0.275936128f, -0.017054561f, -0.106682490f, 0.055976129f },
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{ 0.627245545f, 0.241342015f, -0.016246850f, -0.231302564f, 0.083643275f },
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// distance = 32
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{ 0.562700627f, 0.210158533f, -0.014740899f, -0.357562697f, 0.115680957f },
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{ 0.498787849f, 0.181982455f, -0.012925406f, -0.483461730f, 0.151306628f },
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{ 0.437224055f, 0.156585449f, -0.011055180f, -0.607042210f, 0.189796534f },
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{ 0.379336998f, 0.133834032f, -0.009281617f, -0.726580065f, 0.230469477f },
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// distance = 64
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{ 0.326040627f, 0.113624970f, -0.007683443f, -0.840693542f, 0.272675696f },
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{ 0.277861727f, 0.095845793f, -0.006291936f, -0.948380091f, 0.315795676f },
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{ 0.234997480f, 0.080357656f, -0.005109519f, -1.049001190f, 0.359246807f },
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{ 0.197386484f, 0.066993521f, -0.004122547f, -1.142236313f, 0.402493771f },
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// distance = 128
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{ 0.164780457f, 0.055564709f, -0.003309645f, -1.228023442f, 0.445058962f },
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{ 0.136808677f, 0.045870650f, -0.002646850f, -1.306498037f, 0.486530514f },
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{ 0.113031290f, 0.037708627f, -0.002110591f, -1.377937457f, 0.526566783f },
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{ 0.092980475f, 0.030881892f, -0.001679255f, -1.442713983f, 0.564897095f },
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// distance = 256
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{ 0.076190239f, 0.025205585f, -0.001333863f, -1.501257246f, 0.601319206f },
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{ 0.062216509f, 0.020510496f, -0.001058229f, -1.554025452f, 0.635694228f },
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{ 0.050649464f, 0.016644994f, -0.000838826f, -1.601484205f, 0.667939837f },
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{ 0.041120009f, 0.013475547f, -0.000664513f, -1.644091518f, 0.698022561f },
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// distance = 512
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{ 0.033302044f, 0.010886252f, -0.000526217f, -1.682287704f, 0.725949783f },
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{ 0.026911868f, 0.008777712f, -0.000416605f, -1.716488979f, 0.751761953f },
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{ 0.021705773f, 0.007065551f, -0.000329788f, -1.747083800f, 0.775525335f },
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{ 0.017476603f, 0.005678758f, -0.000261057f, -1.774431204f, 0.797325509f },
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// distance = 1024
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{ 0.014049828f, 0.004558012f, -0.000206658f, -1.798860530f, 0.817261711f },
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{ 0.011279504f, 0.003654067f, -0.000163610f, -1.820672082f, 0.835442043f },
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{ 0.009044384f, 0.002926264f, -0.000129544f, -1.840138412f, 0.851979516f },
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{ 0.007244289f, 0.002341194f, -0.000102586f, -1.857505967f, 0.866988864f },
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// distance = 2048
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{ 0.005796846f, 0.001871515f, -0.000081250f, -1.872996926f, 0.880584038f },
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{ 0.004634607f, 0.001494933f, -0.000064362f, -1.886811124f, 0.892876302f },
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{ 0.003702543f, 0.001193324f, -0.000050993f, -1.899127955f, 0.903972829f },
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{ 0.002955900f, 0.000951996f, -0.000040407f, -1.910108223f, 0.913975712f },
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// distance = 4096
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{ 0.002358382f, 0.000759068f, -0.000032024f, -1.919895894f, 0.922981321f },
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{ 0.001880626f, 0.000604950f, -0.000025383f, -1.928619738f, 0.931079931f },
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{ 0.001498926f, 0.000481920f, -0.000020123f, -1.936394836f, 0.938355560f },
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{ 0.001194182f, 0.000383767f, -0.000015954f, -1.943323983f, 0.944885977f },
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// distance = 8192
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{ 0.000951028f, 0.000305502f, -0.000012651f, -1.949498943f, 0.950742822f },
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{ 0.000757125f, 0.000243126f, -0.000010033f, -1.955001608f, 0.955991826f },
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{ 0.000602572f, 0.000193434f, -0.000007957f, -1.959905036f, 0.960693085f },
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{ 0.000479438f, 0.000153861f, -0.000006312f, -1.964274383f, 0.964901371f },
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// distance = 16384
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{ 0.000381374f, 0.000122359f, -0.000005007f, -1.968167752f, 0.968666478f },
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{ 0.000303302f, 0.000097288f, -0.000003972f, -1.971636944f, 0.972033562f },
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{ 0.000241166f, 0.000077342f, -0.000003151f, -1.974728138f, 0.975043493f },
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{ 0.000191726f, 0.000061475f, -0.000002500f, -1.977482493f, 0.977733194f },
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// distance = 32768
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{ 0.000152399f, 0.000048857f, -0.000001984f, -1.979936697f, 0.980135969f },
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{ 0.000121122f, 0.000038825f, -0.000001574f, -1.982123446f, 0.982281818f },
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{ 0.000096252f, 0.000030849f, -0.000001249f, -1.984071877f, 0.984197728f },
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{ 0.000076480f, 0.000024509f, -0.000000991f, -1.985807957f, 0.985907955f },
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};
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static const float TWOPI = 6.283185307f;
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//
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@ -578,80 +682,58 @@ static void ThiranBiquad(float f, float& b0, float& b1, float& b2, float& a1, fl
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b2 = 1.0f;
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}
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// returns the gain of analog (s-plane) lowpass evaluated at w
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static double analogFilter(double w0, double w) {
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double w0sq, wsq;
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double num, den;
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// split x into exponent and fraction (0.0f to 1.0f)
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static void splitf(float x, int& expn, float& frac) {
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w0sq = w0 * w0;
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wsq = w * w;
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union { float f; int i; } mant, bits = { x };
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const int IEEE754_MANT_BITS = 23;
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const int IEEE754_EXPN_BIAS = 127;
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num = w0sq * w0sq;
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den = wsq * wsq + w0sq * w0sq;
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return sqrt(num / den);
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mant.i = bits.i & ((1 << IEEE754_MANT_BITS) - 1);
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mant.i |= (IEEE754_EXPN_BIAS << IEEE754_MANT_BITS);
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frac = mant.f - 1.0f;
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expn = (bits.i >> IEEE754_MANT_BITS) - IEEE754_EXPN_BIAS;
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}
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// design a lowpass biquad using analog matching
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static void LowpassBiquad(double coef[5], double w0) {
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double G1;
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double wpi, wn, wd;
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double wna, wda;
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double gn, gd, gnsq, gdsq;
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double num, den;
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double Wnsq, Wdsq, B, A;
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double b0, b1, b2, a0, a1, a2;
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double temp, scale;
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const double PI = 3.14159265358979323846;
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static void distanceBiquad(float distance, float& b0, float& b1, float& b2, float& a1, float& a2) {
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// compute the Nyquist gain
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wpi = w0 + 2.8 * (1.0 - w0/PI); // minimax-like error
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wpi = (wpi > PI) ? PI : wpi;
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G1 = analogFilter(w0, wpi);
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//
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// Computed from a lookup table quantized to distance = 2^(N/4)
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// and reconstructed by piecewise linear interpolation.
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// Approximation error < 0.25dB
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//
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// approximate wn and wd
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wd = 0.5 * w0;
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wn = wd * sqrt(1.0/G1); // down G1 at pi, instead of zeros
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float x = distance;
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x = MIN(MAX(x, 1.0f), 1<<30);
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x *= x;
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x *= x; // x = distance^4
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Wnsq = wn * wn;
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Wdsq = wd * wd;
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// split x into e and frac, such that x = 2^(e+0) + frac * (2^(e+1) - 2^(e+0))
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int e;
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float frac;
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splitf(x, e, frac);
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// analog freqs of wn and wd
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wna = 2.0 * atan(wn);
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wda = 2.0 * atan(wd);
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// clamp to table limits
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if (e < 0) {
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e = 0;
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frac = 0.0f;
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}
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if (e > NLOWPASS-2) {
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e = NLOWPASS-2;
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frac = 1.0f;
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}
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assert(frac >= 0.0f);
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assert(frac <= 1.0f);
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assert(e+0 >= 0);
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assert(e+1 < NLOWPASS);
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// normalized analog gains at wna and wda
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temp = 1.0 / G1;
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gn = temp * analogFilter(w0, wna);
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gd = temp * analogFilter(w0, wda);
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gnsq = gn * gn;
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gdsq = gd * gd;
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// compute B, matching gains at wn and wd
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temp = 1.0 / (wn * wd);
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den = fabs(gnsq - gdsq);
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num = gnsq * (Wnsq - Wdsq) * (Wnsq - Wdsq) * (Wnsq + gdsq * Wdsq);
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B = temp * sqrt(num / den);
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// compute A, matching gains at wn and wd
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num = (Wnsq - Wdsq) * (Wnsq - Wdsq) * (Wnsq + gnsq * Wdsq);
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A = temp * sqrt(num / den);
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// design digital filter via bilinear transform
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b0 = G1 * (1.0 + B + Wnsq);
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b1 = G1 * 2.0 * (Wnsq - 1.0);
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b2 = G1 * (1.0 - B + Wnsq);
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a0 = 1.0 + A + Wdsq;
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a1 = 2.0 * (Wdsq - 1.0);
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a2 = 1.0 - A + Wdsq;
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// normalize
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scale = 1.0 / a0;
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coef[0] = b0 * scale;
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coef[1] = b1 * scale;
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coef[2] = b2 * scale;
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coef[3] = a1 * scale;
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coef[4] = a2 * scale;
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// piecewise linear interpolation
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b0 = lowpassTable[e+0][0] + frac * (lowpassTable[e+1][0] - lowpassTable[e+0][0]);
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b1 = lowpassTable[e+0][1] + frac * (lowpassTable[e+1][1] - lowpassTable[e+0][1]);
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b2 = lowpassTable[e+0][2] + frac * (lowpassTable[e+1][2] - lowpassTable[e+0][2]);
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a1 = lowpassTable[e+0][3] + frac * (lowpassTable[e+1][3] - lowpassTable[e+0][3]);
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a2 = lowpassTable[e+0][4] + frac * (lowpassTable[e+1][4] - lowpassTable[e+0][4]);
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}
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// compute new filters for a given azimuth, distance and gain
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@ -739,38 +821,21 @@ static void setFilters(float firCoef[4][HRTF_TAPS], float bqCoef[5][8], int dela
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}
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//
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// Model the frequency-dependent attenuation of sound propogation in air.
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// Fit using linear regression to a log-log model of lowpass cutoff frequency vs distance,
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// loosely based on data from Handbook of Acoustics. Only the onset of significant
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// attenuation is modelled, not the filter slope.
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// Second biquad implements the distance filter.
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//
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// 1m -> -3dB @ 55kHz
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// 10m -> -3dB @ 12kHz
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// 100m -> -3dB @ 2.5kHz
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// 1km -> -3dB @ 0.6kHz
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// 10km -> -3dB @ 0.1kHz
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//
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distance = (distance < 1.0f) ? 1.0f : distance;
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double freq = exp2(-0.666 * log2(distance) + 15.75);
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double coef[5];
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LowpassBiquad(coef, (double)TWOPI * freq / 24000);
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distanceBiquad(distance, b0, b1, b2, a1, a2);
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// TESTING: compute attn at w=pi
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//double num = coef[0] - coef[1] + coef[2];
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//double den = 1.0 - coef[3] + coef[4];
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//double mag = 10 * log10((num * num) / (den * den));
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bqCoef[0][channel+4] = b0;
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bqCoef[1][channel+4] = b1;
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bqCoef[2][channel+4] = b2;
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bqCoef[3][channel+4] = a1;
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bqCoef[4][channel+4] = a2;
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bqCoef[0][channel+4] = (float)coef[0];
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bqCoef[1][channel+4] = (float)coef[1];
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bqCoef[2][channel+4] = (float)coef[2];
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bqCoef[3][channel+4] = (float)coef[3];
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bqCoef[4][channel+4] = (float)coef[4];
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bqCoef[0][channel+5] = (float)coef[0];
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bqCoef[1][channel+5] = (float)coef[1];
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bqCoef[2][channel+5] = (float)coef[2];
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bqCoef[3][channel+5] = (float)coef[3];
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bqCoef[4][channel+5] = (float)coef[4];
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bqCoef[0][channel+5] = b0;
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bqCoef[1][channel+5] = b1;
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bqCoef[2][channel+5] = b2;
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bqCoef[3][channel+5] = a1;
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bqCoef[4][channel+5] = a2;
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}
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void AudioHRTF::render(int16_t* input, float* output, int index, float azimuth, float distance, float gain, int numFrames) {
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