interpreter/preprocessor/faust-0.9.47mr3/architecture/oscillator.lib

   1 declare name "Faust Oscillator Library";
   2 declare author "Julius O. Smith (jos at ccrma.stanford.edu)";
   3 declare copyright "Julius O. Smith III";
   4 declare version "1.10";
   5 declare license "STK-4.3"; // Synthesis Tool Kit 4.3 (MIT style license)
   6
   7 import("music.lib");  // SR, ...
   8 import("filter.lib"); // wgr, nlf2, tf2
   9
  10 //===================== Virtual Analog Oscillators ========================
  11
  12 //------------------------ Impulse Train: imptrain ------------------------
  13 imptrain(freq) = sawpos(freq)<:-(mem)<0;
  14
  15 //--- Pulse-Train and Square-Wave Oscillators: pulsetrainpos, squarewave[pos]
  16 // In all cases, the first pulse jumps to 1 at time 0.
  17
  18 // Basic unit-amplitude nonnegative pulse train with duty cycle between 0 and 1:
  19 pulsetrainpos(freq,duty) = float(sawpos(freq) <= duty);
  20
  21 // Positive square wave = pulse train with 50% duty cycle:
  22 squarewavepos(freq) = pulsetrainpos(freq,0.5);
  23
  24 // Unit amplitude square wave = zero-mean pulse train with 50% duty cycle:
  25 squarewave(freq) = 2*squarewavepos(freq) - 1;
  26
  27 //---------- Sawtooth: rawsaw, sawpos, saw1, saw2, sawtooth -------------
  28
  29 // Sawtooth waveform oscillators for virtual analog synthesis et al.
  30 // The 'simple' versions (rawsaw, sawpos, saw1), are mere samplings of
  31 // the ideal continuous-time ("analog") waveforms.  While simple, the
  32 // aliasing due to sampling is quite audible.  The differentiated
  33 // polynomial waveform family (saw2,
  34
  35 // --- rawsaw ---
  36 // simple sawtooth waveform oscillator between 0 and period in samples:
  37 rawsaw(periodsamps) = (_,periodsamps : fmod) ~ +(1.0);
  38
  39 // --- sawpos ---
  40 // simple sawtooth waveform oscillator between 0 and 1
  41 sawpos(freq) = rawsaw(periodsamps) / periodsamps
  42 with {
  43   periodsamps = float(SR)/freq; // period in samples (not nec. integer)
  44 };
  45
  46 // --- saw1 ---
  47 // simple sawtooth waveform oscillator between -1 and 1
  48 saw1(freq) = 2.0 * sawpos(freq) - 1.0; // zero-mean in [-1,1)
  49
  50 // --- saw2 ---
  51 // Differentiated Parabolic Wave sawtooth (less aliasing)
  52 // Reference: Valimaki, IEEE Signal Processing Letters, March 2005
  53 saw2(freq) = saw1(freq) <: * <: -(mem) : *(0.25'*SR/freq);
  54
  55 // --- sawtooth ---
  56 sawtooth = saw2; // default choice
  57
  58 //-------------------------- sawtooth_demo ---------------------------
  59 // USAGE:  sawtooth_demo : _
  60
  61 sawtooth_demo = signal with {
  62   osc_group(x) = vgroup("[0] SAWTOOTH OSCILLATOR
  63     [tooltip: See Faust's oscillator.lib for documentation and references]",x);
  64   knob_group(x)  = osc_group(hgroup("[1]", x));
  65   ampdb  = knob_group(vslider("[1] Amplitude [unit:dB] [style:knob]
  66     [tooltip: Sawtooth waveform amplitude]",
  67     -20,-120,10,0.1));
  68   amp = ampdb : smooth(0.999) : db2linear;
  69   freq = knob_group(
  70   vslider("[2] Frequency [unit:PK] [style:knob]
  71     [tooltip: Sawtooth frequency as a Piano Key (PK) number (A440 = key 49)]",
  72     49,1,88,0.01) : pianokey2hz);
  73   pianokey2hz(x) = 440.0*pow(2.0, (x-49.0)/12); // piano key 49 = A440 (also defined in effect.lib)
  74   detune1 = 1 + 0.01 * knob_group(
  75     vslider("[3] Detuning 1 [unit:%%] [style:knob]
  76       [tooltip: Percentange frequency-shift up or down for second oscillator]",
  77       -0.1,-10,10,0.01));
  78   detune2 = 1 + 0.01 * knob_group(
  79     vslider("[4] Detuning 2 [unit:%%] [style:knob]
  80 [tooltip: Percentange frequency-shift up or down for third detuned oscillator]",
  81     +0.1,-10,10,0.01));
  82   portamento = knob_group(
  83     vslider("[5] Portamento [unit:sec] [style:knob]
  84       [tooltip: Portamento (frequency-glide) time-constant in seconds]",
  85       0.1,0.01,1,0.001));
  86   sfreq = freq : smooth(tau2pole(portamento));
  87   tone = (amp/3) *
  88     (sawtooth(sfreq) + sawtooth(sfreq*detune1) + sawtooth(sfreq*detune2));
  89   signal = amp * select2(ei, select2(ss, tone, pink_noise), _);
  90   checkbox_group(x) = knob_group(vgroup("[6] Alternate Signals",x));
  91   ss = checkbox_group(checkbox("[0]
  92 [tooltip: Pink Noise (or 1/f noise) is Constant-Q Noise, meaning that it has the same total power in every octave] Pink Noise Instead (uses only Amplitude control on the left)"));
  93   ei = checkbox_group(checkbox(
  94       "[1] External Input Instead (overrides Sawtooth/Noise selection above)"));
  95 };
  96
  97 // --- Correction-filtered versions of saw2: saw2f2, saw2f4 ----
  98 saw2f2 = saw2 : cf2 with {
  99   cf2 = tf2(1.155704605878911, 0.745184288225518,0.040305967265900,
 100         0.823765146386639, 0.117420665547108);
 101 };
 102
 103 saw2f4 = saw2 : cf4 with {
 104   cf4 = iir((1.155727435125014, 2.285861038554662,
 105         1.430915027294021, 0.290713280893317, 0.008306401748854),
 106         (2.156834679164532, 1.559532244409321, 0.423036498118354,
 107         0.032080681130972));
 108 };
 109
 110 // --- sawN, saw3,saw4,saw5,saw6 ---
 111 // Differentiated Polynomial Wave (DPW) sawtooth (progressively less aliasing)
 112 // Reference:
 113 // "Alias-Suppressed Oscillators based on Differentiated Polynomial Waveforms",
 114 // Vesa Valimaki, Juhan Nam, Julius Smith, and Jonathan Abel,
 115 // IEEE Tr. Acoustics, Speech, and Language Processing (IEEE-ASLP),
 116 // Vol. 18, no. 5, May 2010.
 117
 118 sawN(N,freq) = saw1 : poly(N) : D(N-1) : gate(N-1)
 119 with {
 120   p0n = SR/freq;
 121   sawpos = (_,1:fmod) ~ +(1/p0n); // sawtooth waveform in [0,1)
 122   saw1 = 2*sawpos - 1; // zero average mean, unit max amp
 123   poly(2,x) =  x*x;
 124   poly(3,x) =  x*x*x - x;
 125   poly(4,x) =  poly(2,x)*(poly(2,x) - 2);
 126   poly(5,x) =  pow(x,5) - pow(x,3)*10/3 + x*7/3;
 127   poly(6,x) =  pow(x,6) - 5*pow(x,4) + 7*poly(2,x);
 128   diff1(x) =  (x - x')/(2/p0n);
 129   diff(N) = seq(n,N,diff1); // N diffs in series
 130   D(1) = diff1/2;
 131   D(2) = diff(2)/6;
 132   D(3) = diff(3)/24;
 133   D(4) = diff(4)/120;
 134   D(5) = diff(5)/720;
 135   gatedelay(n,d,x)    = x@(int(d)&(n-1)); // from music.lib
 136   gate(N) = * (1 : gatedelay(8,N)); // delayed step for blanking startup glitch
 137 };
 138 saw3 = sawN(3); saw4 = sawN(4); saw5 = sawN(5); saw6 = sawN(6);
 139
 140 //----------------------- Filter-Based Oscillators ------------------------
 141
 142 // Quick Guide (more complete documentation forthcoming):
 143 //
 144 //    USAGE: osc[b|r|rs|rc|s|w](f), where f = frequency in Hz.
 145 //
 146 //  oscb: one-multiply, two-adds, amplitude varies with frequency, avoid dc
 147 //  oscr: four-multipies, two-adds, amplitude unchanging with frequency,
 148 //        dc ok, amp slowly drifts,
 149 //        sine and cosine outputs available (exact phase quadrature)
 150 // oscrs: sine output of oscr
 151 // oscrc: cosine output of oscr
 152 //  oscs: two-multiplies, two-adds, amplitude varies slightly with frequency,
 153 //        dc ok, no amp drift, likely optimizable to be the fastest no-drift case
 154 //  oscw: one/two-multiply, three-adds, amplitude steady with frequency, no amp drift,
 155 //        sine and cosine outputs available (exact phase quadrature),
 156 //        numerical difficulty below 10 Hz,
 157 //        likely optimizable to be best (above 10 Hz) for custom silicon
 158 //        (one multiply when frequency is constant, two otherwise).
 159
 160 impulse = 1-1'; // used to start filter-based oscillators
 161
 162 //-------------------------- oscb --------------------------------
 163 // Sinusoidal oscillator based on the biquad
 164 //
 165 oscb(f) = impulse : tf2(1,0,0,a1,1)
 166 with {
 167   a1 = -2*cos(2*PI*f/SR);
 168 };
 169
 170 //-------------------------- oscr --------------------------------
 171 // Sinusoidal oscillator based on 2D vector rotation,
 172 //  = undamped "coupled-form" resonator
 173 //  = lossless 2nd-order normalized ladder filter
 174 //
 175 // Reference:
 176 // https://ccrma.stanford.edu/~jos/pasp/Normalized_Scattering_Junctions.html
 177 //
 178 oscrq(f) =  impulse : nlf2(f,1); // sine and cosine outputs
 179 oscrs(f) =  impulse : nlf2(f,1) : _,!; // sine
 180 oscrc(f) =  impulse : nlf2(f,1) : !,_; // cosine
 181 oscr = oscrs; // default = sine case
 182
 183 //-------------------------- oscs --------------------------------
 184 // Sinusoidal oscillator based on the state variable filter
 185 // = undamped "modified-coupled-form" resonator
 186 //
 187 oscs(f) =  (*(0-1) : sint(wn) : sintp(wn,impulse)) ~ _
 188 with {
 189   wn = 2*PI*f/SR; // approximate
 190   // wn = 2*sin(PI*f/SR); // exact
 191   sub(x,y) = y-x;
 192   sint(x) = *(x) : + ~ _ ; // frequency-scaled integrator
 193   sintp(x,y) = *(x) : +(y): + ~ _ ; // same + state input
 194 };
 195
 196 //----------------- oscw, oscwq, oscwc, oscws --------------------
 197 // Sinusoidal oscillator based on the waveguide resonator wgr
 198 //
 199 // oscwc - unit-amplitude cosine oscillator
 200 // oscws - unit-amplitude sine oscillator
 201 // oscq  - unit-amplitude cosine and sine (quadrature) oscillator
 202 // oscw  - default = oscwc for maximum speed
 203 //
 204 // Reference:
 205 // https://ccrma.stanford.edu/~jos/pasp/Digital_Waveguide_Oscillator.html
 206 //
 207 oscwc(fr) = impulse : wgr(fr,1) : _,!; // cosine (cheapest at 1 mpy/sample)
 208 oscws(fr) = impulse : wgr(fr,1) : !,_; // sine (needs a 2nd scaling mpy)
 209 oscq(fr)  = impulse : wgr(fr,1);       // phase quadrature outputs
 210 oscw = oscwc;
 211
 212 //-------------------------- oscrs_demo ---------------------------
 213
 214 oscrs_demo = signal with {
 215   osc_group(x) = vgroup("[0] SINE WAVE OSCILLATOR oscrs
 216     [tooltip: Sine oscillator based on 2D vector rotation]",x);
 217   knob_group(x)  = osc_group(hgroup("[1]", x));
 218 //  ampdb  = knob_group(vslider("[1] Amplitude [unit:dB] [style:knob]
 219   ampdb  = knob_group(hslider("[1] Amplitude [unit:dB]
 220     [tooltip: Sawtooth waveform amplitude]",
 221     -20,-120,10,0.1));
 222   amp = ampdb : smooth(0.999) : db2linear;
 223   freq = knob_group(
 224 //  vslider("[2] Frequency [unit:PK] [style:knob]
 225   hslider("[2] Frequency [unit:PK]
 226      [tooltip: Sine wave frequency as a Piano Key (PK) number (A440 = 49 PK)]",
 227      49,1,88,0.01) : pianokey2hz);
 228   pianokey2hz(x) = 440.0*pow(2.0, (x-49.0)/12); // (also defined in effect.lib)
 229   portamento = knob_group(
 230 //    vslider("[3] Portamento [unit:sec] [style:knob]
 231     hslider("[3] Portamento [unit:sec]
 232       [tooltip: Portamento (frequency-glide) time-constant in seconds]",
 233       0.1,0,1,0.001));
 234   sfreq = freq : smooth(tau2pole(portamento));
 235   signal = amp * oscrs(sfreq);
 236 };
 237
 238 oscr_demo = oscrs_demo; // synonym
 239
 240 //--------------------------- pink_noise --------------------------
 241 // Pink noise (1/f noise) generator (third-order approximation)
 242 //
 243 // USAGE: pink_noise : _;
 244 //
 245 // Reference:
 246 //  https://ccrma.stanford.edu/~jos/sasp/Example_Synthesis_1_F_Noise.html
 247 //
 248
 249 pink_noise = noise :
 250    iir((0.049922035, -0.095993537, 0.050612699, -0.004408786),
 251                     (-2.494956002, 2.017265875, -0.522189400));