Signal Processing Libraries for F AUST Julius Smith CCRMA, Stanford University Linux Audio Conference 2012 (LAC-12) April 14, 2012 Julius Smith LAC-12 – 1 / 30
Overview effect.lib filter.lib oscillator.lib Conclusion Overview Julius Smith LAC-12 – 2 / 30
F AUST Signal Processing Libraries Overview • oscillator.lib — signal sources effect.lib filter.lib • filter.lib — general-purpose digital filters oscillator.lib • effect.lib — digital audio effects Conclusion Julius Smith LAC-12 – 3 / 30
Highlights of Additions Since LAC-08 Overview • oscillator.lib effect.lib filter.lib ◦ Filter-Based Sinusoid Generators oscillator.lib ◦ Alias-Suppressed Classic Waveform Generators Conclusion • filter.lib ◦ Ladder/Lattice Digital Filters ◦ Audio Filter Banks • effect.lib ◦ Biquad-Based Moog VCFs ◦ Phasing/Flanging/Compression ◦ Artificial Reverberation Julius Smith LAC-12 – 4 / 30
Overview effect.lib filter.lib oscillator.lib Conclusion effect.lib Julius Smith LAC-12 – 5 / 30
Moog Voltage Controlled Filters (VCF) Overview • moog vcf 2b = ideal Moog VCF transfer function factored effect.lib into second-order “biquad” sections • Moog VCF • phasing/flanging • reverberation ◦ Static frequency response is more accurate than filter.lib moog vcf (which has an unwanted one-sample delay in oscillator.lib its feedback path) Conclusion ◦ Coefficient formulas are more complex when one or both parameters are varied • moog vcf 2bn = same but using normalized ladder biquads ◦ Super-robust to time-varying resonant-frequency changes (no pops!) ◦ See F AUST example vcf wah pedals.dsp Julius Smith LAC-12 – 6 / 30
Moog VCF See F AUST example vcf wah pedals.dsp Moog VCF moog vcf(res,fr) analog-form Moog VCF res = corner-resonance amount [0-1] fr = corner-resonance frequency in Hz moog vcf 2b(res,fr) Moog VCF implemented as two biquads ( tf2 ) moog vcf 2bn(res,fr) two protected, normalized-ladder biquads ( tf2np ) Julius Smith LAC-12 – 7 / 30
Phasing and Flanging See F AUST example phaser flanger.dsp Phasing and Flanging vibrato2 mono(...) modulated allpass-chain (see effect.lib for usage) phaser2 mono(...) phasing based on 2nd-order allpasses (see effect.lib fo phaser2 stereo(...) stereo phaser based on 2nd-order allpass chains flanger mono(...) mono flanger flanger stereo(...) stereo flanger Julius Smith LAC-12 – 8 / 30
Artificial Reverberation ( effect.lib ) Overview • General Feedback Delay Network (FDN) Reverberation effect.lib • Moog VCF • phasing/flanging See F AUST example reverb designer.dsp • reverberation filter.lib oscillator.lib • Zita-Rev1 Reverb (FDN+Schroeder) by Fons Adriaensen Conclusion (ported to F AUST ) See F AUST example zita rev1.dsp Julius Smith LAC-12 – 9 / 30
Overview effect.lib filter.lib oscillator.lib Conclusion filter.lib Julius Smith LAC-12 – 10 / 30
Ladder/Lattice Digital Filters ( filter.lib ) Overview • Ladder and lattice digital filters have superior numerical effect.lib properties filter.lib • ladder/lattice • Arbitrary Order (thanks to pattern matching in F AUST ) • normalized ladder • filter banks oscillator.lib • Arbitrary (Stable) Poles and Zeros Conclusion • All Four Major Types: ◦ Kelly-Lochbaum Ladder Filter ◦ One-Multiply Lattice Filter ◦ Two-Multiply Lattice Filter ◦ Normalized Ladder Filter Julius Smith LAC-12 – 11 / 30
Normalized Ladder Digital Filters ( filter.lib ) Overview Advantages of the Normalized Ladder Filter Structure: effect.lib filter.lib • Signal Power Invariant wrt Coefficient Variation • ladder/lattice • normalized ladder ⇒ Extreme Modulation is Safe • filter banks oscillator.lib • Super-Solid Biquad (sweep it as fast as you want!): Conclusion tf2snp() “transfer function, 2nd-order, s-plane, normalized, protected” • See F AUST example vcf wah pedals.dsp Julius Smith LAC-12 – 12 / 30
Ladder and Lattice Digital Filters Lattice/Ladder Filters iir lat2(bcoeffs,acoeffs) two-multiply lattice digital filter iir kl(bcoeffs,acoeffs) Kelly-Lochbaum ladder digital filter iir lat1(bcoeffs,acoeffs) one-multiply lattice digital filter iir nl(bcoeffs,acoeffs) normalized ladder digital filter tf2np(b0,b1,b2,a1,a2) biquad based on stabilized second-order normalized ladder filter nlf2(f,r) second-order normalized ladder digital filter special API Julius Smith LAC-12 – 13 / 30
Block Diagrams Overview import("filter.lib"); effect.lib filter.lib bcoeffs = (1,2,3); • ladder/lattice • normalized ladder acoeffs = (0.1,0.2); • filter banks oscillator.lib process = impulse <: Conclusion iir(bcoeffs,acoeffs), iir_lat2(bcoeffs,acoeffs), iir_kl(bcoeffs,acoeffs), iir_lat1(bcoeffs,acoeffs) :> _; Julius Smith LAC-12 – 14 / 30
Audio Filter Banks ( filter.lib ) Overview • “Analyzer” ∆ = Power-Complementary Band-Division effect.lib ( e.g. , for Spectral Display) filter.lib • ladder/lattice • normalized ladder See F AUST example spectral level.dsp • filter banks oscillator.lib Conclusion • “Filterbank ∆ = Allpass-Complementary Band-Division (Bands Summable Without Notch Formation) See F AUST example graphic eq.dsp • Filterbanks in filter.lib are implemented as analyzers in cascade with delay equalizers that convert the (power-complementary) analyzer to an (allpass-complementary) filter bank Julius Smith LAC-12 – 15 / 30
Overview effect.lib filter.lib oscillator.lib Conclusion oscillator.lib Julius Smith LAC-12 – 16 / 30
oscillator.lib Overview Reference implementations of elementary signal generators: effect.lib filter.lib • sinusoids (filter-based) oscillator.lib • sinusoids • sawtooth (bandlimited) • oscb • oscr ◦ pulse-train = saw minus delayed saw • oscs • oscw ◦ square = 50% duty-cycle pulse-train • virtual analog • sawN ◦ triangle = (leakily) integrated square • sawtooth examples • pink noise ◦ impulse-train = differentiated saw Conclusion ◦ (all alias-suppressed) • pink-noise ( 1 /f noise) Julius Smith LAC-12 – 17 / 30
Sinusoid Generators in oscillator.lib Overview oscb “biquad” two-pole filter section effect.lib (impulse response) filter.lib oscr 2D vector rotation oscillator.lib (second-order normalized ladder) • sinusoids • oscb provides sine and cosine outputs • oscr • oscs oscrs sine output of oscr • oscw oscrc cosine output of oscr • virtual analog • sawN oscs state variable osc., cosine output • sawtooth examples (modified coupled form resonator) • pink noise oscw Conclusion digital waveguide oscillator oscws sine output of oscw oscwc cosine output of oscw Julius Smith LAC-12 – 18 / 30
Block Diagrams Overview Inspect the following test program: effect.lib filter.lib oscillator.lib import("oscillator.lib"); • sinusoids • oscb • oscr freq = 100; • oscs • oscw • virtual analog process = oscb(freq), • sawN • sawtooth examples oscrs(freq), • pink noise oscs(freq), Conclusion oscws(freq); Julius Smith LAC-12 – 19 / 30
Sinusoidal Oscillator oscb oscb (impulsed direct-form biquad) Overview effect.lib • One multiply and two adds per sample of output filter.lib oscillator.lib • Amplitude varies strongly with frequency • sinusoids • oscb • oscr • Numerically poor toward freq=0 (“dc”) • oscs • oscw • virtual analog • Nice choice for high, fixed frequencies • sawN • sawtooth examples • pink noise Conclusion Julius Smith LAC-12 – 20 / 30
Sinusoidal Oscillator oscr oscr (2D vector rotation) Overview effect.lib • Four multiplies and two adds per sample filter.lib oscillator.lib • Amplitude is invariant wrt frequency • sinusoids • oscb • oscr • Good down to dc • oscs • oscw • virtual analog • In-phase (cosine) and phase-quadrature (sine) outputs • sawN • sawtooth examples • Amplitude drifts over long durations at most frequencies • pink noise (coefficients are roundings of s = sin(2*PI*freq/SR) Conclusion and c = cos(2*PI*freq/SR) , so s 2 + c 2 � = 1 ) • Nice for rapidly varying frequencies Julius Smith LAC-12 – 21 / 30
Sinusoidal Oscillator oscs oscs (digitized “state variable filter”) Overview effect.lib • “Magic Circle Algorithm” in computer graphics filter.lib oscillator.lib • Two multiplies and two additions per output sample • sinusoids • oscb • oscr • Amplitude varies much less with frequency than oscr • oscs • oscw • virtual analog • Good down to dc • sawN • sawtooth examples • No long-term amplitude drift • pink noise Conclusion • In-phase and quadrature components available at low frequencies (exact at dc) • Nice lower-cost replacement for oscr when amplitude can vary slightly with frequency, and exact phase-quadrature outputs are not needed Julius Smith LAC-12 – 22 / 30
Recommend
More recommend
