forked from grame-cncm/faustlibraries
-
Notifications
You must be signed in to change notification settings - Fork 0
/
oscillators.lib
2016 lines (1815 loc) · 59 KB
/
oscillators.lib
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
//############################## oscillators.lib ######################################
// This library contains a collection of sound generators. Its official prefix is `os`.
//
// The oscillators library is organized into 9 sections:
//
// * [Wave-Table-Based Oscillators](#wave-table-based-oscillators)
// * [Low Frequency Oscillators](#low-frequency-oscillators)
// * [Low Frequency Sawtooths](#low-frequency-sawtooths)
// * [Alias-Suppressed Sawtooth](#alias-suppressed-sawtooth)
// * [Alias-Suppressed Pulse, Square, and Impulse Trains](#alias-suppressed-pulse-square-and-impulse-trains)
// * [Filter-Based Oscillators](#filter-based-oscillators)
// * [Waveguide-Resonator-Based Oscillators](#waveguide-resonator-based-oscillators)
// * [Casio CZ Oscillators](#casio-cz-oscillators)
// * [PolyBLEP-Based Oscillators](#polyblep-based-oscillators)
//
// #### References
// * <https://github.com/grame-cncm/faustlibraries/blob/master/oscillators.lib>
//########################################################################################
/************************************************************************
************************************************************************
FAUST library file, GRAME section
Except where noted otherwise, Copyright (C) 2003-2017 by GRAME,
Centre National de Creation Musicale.
----------------------------------------------------------------------
GRAME LICENSE
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as
published by the Free Software Foundation; either version 2.1 of the
License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA.
EXCEPTION TO THE LGPL LICENSE : As a special exception, you may create a
larger FAUST program which directly or indirectly imports this library
file and still distribute the compiled code generated by the FAUST
compiler, or a modified version of this compiled code, under your own
copyright and license. This EXCEPTION TO THE LGPL LICENSE explicitly
grants you the right to freely choose the license for the resulting
compiled code. In particular the resulting compiled code has no obligation
to be LGPL or GPL. For example you are free to choose a commercial or
closed source license or any other license if you decide so.
************************************************************************
************************************************************************/
ma = library("maths.lib");
ba = library("basics.lib");
fi = library("filters.lib");
si = library("signals.lib");
declare name "Faust Oscillator Library";
declare version "1.5.1";
// This library contains platform specific constants
pl = library("platform.lib");
//======================Oscillators based on mathematical functions===============
//
// Note that there is a numerical problem with several phasor functions built using the internal
// `phasor_imp`. The reason is that the incremental step is smaller than `ma.EPSILON`, which happens with very small frequencies,
// so it will have no effect when summed to 1, but it will be enough to make the fractional function wrap
// around when summed to 0. An example of this problem can be observed when running the following code:
//
// `process = os.phasor(1.0, -.001);`
//
// The output of this program is the sequence 1, 0, 1, 0, 1... This happens because the negative incremental
// step is greater than `-ma.EPSILON`, which will have no effect when summed to 1, but it will be significant
// enough to make the fractional function wrap around when summed to 0.
//
// The incremental step can be clipped to guarantee that the phasor will
// always run correctly for its full cycle, otherwise, for increments smaller than `ma.EPSILON`,
// phasor would initially run but it'd eventually get stuck once the output gets big enough.
//
// All functions using `phasor_imp` are affected by this problem, but a safer
// version is implemented, and can be used alternatively by setting `SAFE=1` in the environment using
// [explicit sustitution](https://faustdoc.grame.fr/manual/syntax/#explicit-substitution) syntax.
//
// For example: `process = os[SAFE=1;].phasor(1.0, -.001);` will use the safer implementation of `phasor_imp`.
//=================================================================================
//=========================Wave-Table-Based Oscillators===================================
// Oscillators using tables. The table size is set by the
// [pl.tablesize](https://github.com/grame-cncm/faustlibraries/blob/master/platform.lib) constant.
//========================================================================================
// Global parameter to use the safer version of `phasor_imp`, but which
// could be used in other functions as well.
SAFE = 0; // 0: use the faster version, 1: use the safer version
//-----------------------`(os.)sinwaveform`------------------------
// Sine waveform ready to use with a `rdtable`.
//
// #### Usage
//
// ```
// sinwaveform(tablesize) : _
// ```
//
// Where:
//
// * `tablesize`: the table size
//------------------------------------------------------------
sinwaveform(tablesize) =
sin(float(ba.period(tablesize)) * (2.0 * ma.PI) / float(tablesize));
//-----------------------`(os.)coswaveform`------------------------
// Cosine waveform ready to use with a `rdtable`.
//
// #### Usage
//
// ```
// coswaveform(tablesize) : _
// ```
//
// Where:
//
// * `tablesize`: the table size
//------------------------------------------------------------
coswaveform(tablesize) =
cos(float(ba.period(tablesize)) * (2.0 * ma.PI) / float(tablesize));
// Possibly faster version using integer arithmetic
phasor_env(freq, N) = environment {
//------- GLOBAL PARAMS
nbits = 31;
tablesize = 1<<N;
accuracy = int(nbits - N);
mask = (1<<nbits)-1;
inc(step) = int(tablesize * step * (1<<accuracy));
//------- LAMBDA DSP CASE
lambda(inc_op) = (inc_op : &(mask)) ~ _ : >>(accuracy) : /(tablesize);
//------- MINIMAL CASE
hsp(0,0) = lambda(+(inc(freq/ma.SR)'));
//------- GENERAL CASE
hsp(reset,phase) = lambda(select2(hard_reset,+(inc(freq/ma.SR)),inc(phase)))
with {
hard_reset = (1-1')|reset;
};
};
declare phasor_env author "Pierre Mascarade Relano, Maxime Sirbu, Stéphane Letz";
// Generic phasor with `reset` and `phase` parameters to be specialised in concrete use-cases.
phasor_imp(freq, reset, phase) = (select2(hard_reset, +(incr(SAFE)), phase) : ma.decimal) ~ _
with {
incr_aux = freq/ma.SR;
// Faster but less accurate version
incr(0) = incr_aux;
// To make sure that the incremental step is greater or equal to EPSILON or
// less than or equal to -EPSILON to avoid numerical problems.
// A frequency of 0Hz can still be used to freeze the phasor.
incr(1)= (freq != 0) * ba.if(freq < 0, min(-1.0 * ma.EPSILON, incr_aux), max(ma.EPSILON, incr_aux));
// To correctly start at `phase` at the first sample
hard_reset = (1-1')|reset;
};
// Possibly faster version using integer arithmetic
// phasor_imp(freq, reset, phase) = phasor_env(freq, 16).hsp(reset, phase);
// Version to be used with tables
phasor_table(tablesize, freq, reset, phase) = phasor_imp(freq, reset, phase) : *(float(tablesize));
//-----------------------`(os.)phasor`------------------------
// A simple phasor to be used with a `rdtable`.
// `phasor` is a standard Faust function.
//
// #### Usage
//
// ```
// phasor(tablesize,freq) : _
// ```
//
// Where:
//
// * `tablesize`: the table size
// * `freq`: the frequency in Hz
//
// Note that `tablesize` is just a multiplier for the output of a unit-amp phasor
// so `phasor(1.0, freq)` can be used to generate a phasor output in the range [0, 1[.
//------------------------------------------------------------
phasor(tablesize, freq) = phasor_table(tablesize, freq, 0, 0);
//-----------------------`(os.)hs_phasor`------------------------
// Hardsyncing phasor to be used with a `rdtable`.
//
// #### Usage
//
// ```
// hs_phasor(tablesize,freq,reset) : _
// ```
//
// Where:
//
// * `tablesize`: the table size
// * `freq`: the frequency in Hz
// * `reset`: a reset signal, reset phase to 0 when equal to 1
//---------------------------------------------------------
declare hs_phasor author "Mike Olsen, revised by Stéphane Letz";
hs_phasor(tablesize, freq, reset) = phasor_table(tablesize, freq, reset, 0);
//-----------------------`(os.)hsp_phasor`------------------------
// Hardsyncing phasor with selectable phase to be used with a `rdtable`.
//
// #### Usage
//
// ```
// hsp_phasor(tablesize,freq,reset,phase)
// ```
//
// Where:
//
// * `tablesize`: the table size
// * `freq`: the frequency in Hz
// * `reset`: reset the oscillator to phase when equal to 1
// * `phase`: phase between 0 and 1
//---------------------------------------------------------
declare hsp_phasor author "Christophe Lebreton, revised by Stéphane Letz";
hsp_phasor(tablesize, freq, reset, phase) = phasor_table(tablesize, freq, reset, phase);
//-----------------------`(os.)oscsin`------------------------
// Sine wave oscillator.
// `oscsin` is a standard Faust function.
//
// #### Usage
//
// ```
// oscsin(freq) : _
// ```
//
// Where:
//
// * `freq`: the frequency in Hz
//------------------------------------------------------------
oscsin(freq) = rdtable(tablesize, sinwaveform(tablesize), int(phasor(tablesize,freq)))
with {
tablesize = pl.tablesize;
};
//-----------------------`(os.)hs_oscsin`------------------------
// Sin lookup table with hardsyncing phase.
//
// #### Usage
//
// ```
// hs_oscsin(freq,reset) : _
// ```
//
// Where:
//
// * `freq`: the frequency in Hz
// * `reset`: reset the oscillator to 0 when equal to 1
//---------------------------------------------------------
declare hs_oscsin author "Mike Olsen";
hs_oscsin(freq,reset) = rdtable(tablesize, sinwaveform(tablesize), int(hs_phasor(tablesize,freq,reset)))
with {
tablesize = pl.tablesize;
};
//-----------------------`(os.)osccos`------------------------
// Cosine wave oscillator.
//
// #### Usage
//
// ```
// osccos(freq) : _
// ```
//
// Where:
//
// * `freq`: the frequency in Hz
//------------------------------------------------------------
osccos(freq) = rdtable(tablesize, coswaveform(tablesize), int(phasor(tablesize,freq)))
with {
tablesize = pl.tablesize;
};
//-----------------------`(os.)hs_osccos`------------------------
// Cos lookup table with hardsyncing phase.
//
// #### Usage
//
// ```
// hs_osccos(freq,reset) : _
// ```
//
// Where:
//
// * `freq`: the frequency in Hz
// * `reset`: reset the oscillator to 0 when equal to 1
//---------------------------------------------------------
declare hs_osccos author "Stéphane Letz";
hs_osccos(freq,reset) = rdtable(tablesize, coswaveform(tablesize), int(hs_phasor(tablesize,freq,reset)))
with {
tablesize = pl.tablesize;
};
//-----------------------`(os.)oscp`------------------------
// A sine wave generator with controllable phase.
//
// #### Usage
//
// ```
// oscp(freq,phase) : _
// ```
//
// Where:
//
// * `freq`: the frequency in Hz
// * `phase`: the phase in radian
//------------------------------------------------------------
oscp(freq,phase) = oscsin(freq) * cos(phase) + osccos(freq) * sin(phase);
//-----------------------`(os.)osci`------------------------
// Interpolated phase sine wave oscillator.
//
// #### Usage
//
// ```
// osci(freq) : _
// ```
//
// Where:
//
// * `freq`: the frequency in Hz
//------------------------------------------------------------
osci(freq) = s1 + d * (s2 - s1)
with {
tablesize = pl.tablesize;
i = int(phasor(tablesize,freq));
d = ma.decimal(phasor(tablesize,freq));
s1 = rdtable(tablesize+1,sinwaveform(tablesize),i);
s2 = rdtable(tablesize+1,sinwaveform(tablesize),i+1);
};
//-----------------------`(os.)osc`------------------------
// Default sine wave oscillator (same as [oscsin](#oscsin)).
// `osc` is a standard Faust function.
//
// #### Usage
//
// ```
// osc(freq) : _
// ```
//
// Where:
//
// * `freq`: the frequency in Hz
//------------------------------------------------------------
osc = oscsin;
//-----------------------`(os.)m_oscsin`------------------------
// Sine wave oscillator based on the `sin` mathematical function.
//
// #### Usage
//
// ```
// m_oscsin(freq) : _
// ```
//
// Where:
//
// * `freq`: the frequency in Hz
//------------------------------------------------------------
m_oscsin(freq) = lf_sawpos(freq) : *(2*ma.PI) : sin;
//-----------------------`(os.)m_osccos`------------------------
// Sine wave oscillator based on the `cos` mathematical function.
//
// #### Usage
//
// ```
// m_osccos(freq) : _
// ```
//
// Where:
//
// * `freq`: the frequency in Hz
//------------------------------------------------------------
m_osccos(freq) = lf_sawpos(freq) : *(2*ma.PI) : cos;
// end GRAME section
//########################################################################################
/************************************************************************
FAUST library file, jos section
Except where noted otherwise, The Faust functions below in this
section are Copyright (C) 2003-2022 by Julius O. Smith III <[email protected]>
([jos](http://ccrma.stanford.edu/~jos/)), and released under the
(MIT-style) [STK-4.3](#stk-4.3-license) license.
The MarkDown comments in this section are Copyright 2016-2017 by Romain
Michon and Julius O. Smith III, and are released under the
[CCA4I](https://creativecommons.org/licenses/by/4.0/) license (TODO: if/when Romain agrees)
************************************************************************/
//===============================Low Frequency Oscillators===============================
// Low Frequency Oscillators (LFOs) have prefix `lf_`
// (no aliasing suppression, since it is inaudible at LF).
// Use `sawN` and its derivatives for audio oscillators with suppressed aliasing.
//==================================================================
//--------`(os.)lf_imptrain`----------
// Unit-amplitude low-frequency impulse train.
// `lf_imptrain` is a standard Faust function.
// #### Usage
//
// ```
// lf_imptrain(freq) : _
// ```
// Where:
//
// * `freq`: frequency in Hz
//------------------------------------------------------------
lf_imptrain(freq) = lf_sawpos(freq)<:-(mem)<0; // definition below
//--------`(os.)lf_pulsetrainpos`----------
// Unit-amplitude nonnegative LF pulse train, duty cycle between 0 and 1.
//
//
// #### Usage
//
// ```
// lf_pulsetrainpos(freq, duty) : _
// ```
//
// Where:
//
// * `freq`: frequency in Hz
// * `duty`: duty cycle between 0 and 1
//------------------------------------------------------------
lf_pulsetrainpos(freq,duty) = float(lf_sawpos(freq) <= duty);
//pulsetrainpos = lf_pulsetrainpos; // for backward compatibility
//--------`(os.)lf_pulsetrain`----------
// Unit-amplitude zero-mean LF pulse train, duty cycle between 0 and 1.
//
// #### Usage
//
// ```
// lf_pulsetrain(freq,duty) : _
// ```
//
// Where:
//
// * `freq`: frequency in Hz
// * `duty`: duty cycle between 0 and 1
//------------------------------------------------------------
lf_pulsetrain(freq,duty) = 2.0*lf_pulsetrainpos(freq,duty) - 1.0;
//--------`(os.)lf_squarewavepos`----------
// Positive LF square wave in [0,1]
//
// #### Usage
//
// ```
// lf_squarewavepos(freq) : _
// ```
//
// Where:
//
// * `freq`: frequency in Hz
//------------------------------------------------------------
lf_squarewavepos(freq) = lf_pulsetrainpos(freq,0.5);
// squarewavepos = lf_squarewavepos; // for backward compatibility
//--------`(os.)lf_squarewave`----------
// Zero-mean unit-amplitude LF square wave.
// `lf_squarewave` is a standard Faust function.
//
// #### Usage
//
// ```
// lf_squarewave(freq) : _
// ```
//
// Where:
//
// * `freq`: frequency in Hz
//------------------------------------------------------------
lf_squarewave(freq) = 2.0*lf_squarewavepos(freq) - 1.0;
// squarewave = lf_squarewave; // for backward compatibility
//--------`(os.)lf_trianglepos`----------
// Positive unit-amplitude LF positive triangle wave.
//
// #### Usage
//
// ```
// lf_trianglepos(freq) : _
// ```
//
// Where:
//
// * `freq`: frequency in Hz
//------------------------------------------------------------
lf_trianglepos(freq) = 1.0-abs(saw1(freq)); // saw1 defined below
//----------`(os.)lf_triangle`----------
// Zero-mean unit-amplitude LF triangle wave.
// `lf_triangle` is a standard Faust function.
//
// #### Usage
//
// ```
// lf_triangle(freq) : _
// ```
//
// Where:
//
// * `freq`: frequency in Hz
//------------------------------------------------------------
declare lf_triangle author "Bart Brouns";
declare lf_triangle licence "STK-4.3";
lf_triangle(freq) = 2.0*lf_trianglepos(freq) - 1.0;
//================== Low Frequency Sawtooths ====================
// Sawtooth waveform oscillators for virtual analog synthesis et al.
// The 'simple' versions (`lf_rawsaw`, `lf_sawpos` and `saw1`), are mere samplings of
// the ideal continuous-time ("analog") waveforms. While simple, the
// aliasing due to sampling is quite audible. The differentiated
// polynomial waveform family (`saw2`, `sawN`, and derived functions)
// do some extra processing to suppress aliasing (not audible for
// very low fundamental frequencies). According to Lehtonen et al.
// (JASA 2012), the aliasing of `saw2` should be inaudible at fundamental
// frequencies below 2 kHz or so, for a 44.1 kHz sampling rate and 60 dB SPL
// presentation level; fundamentals 415 and below required no aliasing
// suppression (i.e., `saw1` is ok).
//=====================================================================
//-----------------`(os.)lf_rawsaw`--------------------
// Simple sawtooth waveform oscillator between 0 and period in samples.
//
// #### Usage
//
// ```
// lf_rawsaw(periodsamps) : _
// ```
//
// Where:
//
// * `periodsamps`: number of periods per samples
//---------------------------------------------------------
lf_rawsaw(periodsamps) = (_,periodsamps : fmod) ~ +(1.0);
//-----------------`(os.)lf_sawpos`--------------------
// Simple sawtooth waveform oscillator between 0 and 1.
//
// #### Usage
//
// ```
// lf_sawpos(freq) : _
// ```
//
// Where:
//
// * `freq`: frequency in Hz
//
//---------------------------------------------------------
declare lf_sawpos author "Bart Brouns, revised by Stéphane Letz";
declare lf_sawpos licence "STK-4.3";
lf_sawpos(freq) = phasor_imp(freq, 0, 0);
//-----------------`(os.)lf_sawpos_phase`--------------------
// Simple sawtooth waveform oscillator between 0 and 1
// with phase control.
//
// #### Usage
//
// ```
// lf_sawpos_phase(freq, phase) : _
// ```
//
// Where:
//
// * `freq`: frequency in Hz
// * `phase`: phase between 0 and 1
//---------------------------------------------------------
declare lf_sawpos_phase author "Bart Brouns, revised by Stéphane Letz";
declare lf_sawpos_phase licence "STK-4.3";
lf_sawpos_phase(freq,phase) = phasor_imp(freq, 0, phase);
//-----------------`(os.)lf_sawpos_reset`--------------------
// Simple sawtooth waveform oscillator between 0 and 1
// with reset.
//
// #### Usage
//
// ```
// lf_sawpos_reset(freq,reset) : _
// ```
//
// Where:
//
// * `freq`: frequency in Hz
// * `reset`: reset the oscillator to 0 when equal to 1
//
//---------------------------------------------------------
declare lf_sawpos_reset author "Bart Brouns, revised by Stéphane Letz";
declare lf_sawpos_reset licence "STK-4.3";
lf_sawpos_reset(freq,reset) = phasor_imp(freq, reset, 0);
//-----------------`(os.)lf_sawpos_phase_reset`--------------------
// Simple sawtooth waveform oscillator between 0 and 1
// with phase control and reset.
//
// #### Usage
//
// ```
// lf_sawpos_phase_reset(freq,phase,reset) : _
// ```
//
// Where:
//
// * `freq`: frequency in Hz
// * `phase`: phase between 0 and 1
// * `reset`: reset the oscillator to phase when equal to 1
//
//---------------------------------------------------------
declare lf_sawpos_phase_reset author "Bart Brouns, revised by Stéphane Letz";
declare lf_sawpos_phase_reset licence "STK-4.3";
lf_sawpos_phase_reset(freq,phase,reset) = phasor_imp(freq, reset, phase);
//-----------------`(os.)lf_saw`--------------------
// Simple sawtooth waveform oscillator between -1 and 1.
// `lf_saw` is a standard Faust function.
//
// #### Usage
//
// ```
// lf_saw(freq) : _
// ```
//
// Where:
//
// * `freq`: frequency in Hz
//---------------------------------------------------------
declare saw1 author "Bart Brouns";
declare saw1 licence "STK-4.3";
saw1(freq) = 2.0 * lf_sawpos(freq) - 1.0;
lf_saw(freq) = saw1(freq);
//================== Alias-Suppressed Sawtooth ====================
//-----------------`(os.)sawN`--------------------
// Alias-Suppressed Sawtooth Audio-Frequency Oscillator using Nth-order polynomial transitions
// to reduce aliasing.
//
// `sawN(N,freq)`, `sawNp(N,freq,phase)`, `saw2dpw(freq)`, `saw2(freq)`, `saw3(freq)`,
// `saw4(freq)`, `sawtooth(freq)`, `saw2f2(freq)`, `saw2f4(freq)`
//
// #### Usage
//
// ```
// sawN(N,freq) : _ // Nth-order aliasing-suppressed sawtooth using DPW method (see below)
// sawNp(N,freq,phase) : _ // sawN with phase offset feature
// saw2dpw(freq) : _ // saw2 using DPW
// saw2ptr(freq) : _ // saw2 using the faster, stateless PTR method
// saw2(freq) : _ // DPW method, but subject to change if a better method emerges
// saw3(freq) : _ // sawN(3)
// saw4(freq) : _ // sawN(4)
// sawtooth(freq) : _ // saw2
// saw2f2(freq) : _ // saw2dpw with 2nd-order droop-correction filtering
// saw2f4(freq) : _ // saw2dpw with 4th-order droop-correction filtering
// ```
//
// Where:
//
// * `N`: polynomial order, a constant numerical expression between 1 and 4
// * `freq`: frequency in Hz
// * `phase`: phase between 0 and 1
//
// #### Method
// Differentiated Polynomial Wave (DPW).
//
// ##### Reference
// "Alias-Suppressed Oscillators based on Differentiated Polynomial Waveforms",
// Vesa Valimaki, Juhan Nam, Julius Smith, and Jonathan Abel,
// IEEE Tr. Audio, Speech, and Language Processing (IEEE-ASLP),
// Vol. 18, no. 5, pp 786-798, May 2010.
// 10.1109/TASL.2009.2026507.
//
// #### Notes
// The polynomial order `N` is limited to 4 because noise has been
// observed at very low `freq` values. (LFO sawtooths should of course
// be generated using `lf_sawpos` instead.)
//-----------------------------------------------------------------
declare sawN author "Julius O. Smith III";
declare sawN license "STK-4.3";
// --- sawN for N = 1 to 4 ---
// Orders 5 and 6 have noise at low fundamentals: MAX_SAW_ORDER = 6; MAX_SAW_ORDER_NEXTPOW2 = 8;
MAX_SAW_ORDER = 4;
MAX_SAW_ORDER_NEXTPOW2 = 8; // par cannot handle the case of 0 elements
sawN(N,freq) = saw1l : poly(Nc) : D(Nc-1) : gate(Nc-1)
with {
Nc = max(1,min(N,MAX_SAW_ORDER));
clippedFreq = max(20.0,abs(freq)); // use lf_sawpos(freq) for LFOs (freq < 20 Hz)
saw1l = 2*lf_sawpos(clippedFreq) - 1; // zero-mean, amplitude +/- 1
poly(1,x) = x;
poly(2,x) = x*x;
poly(3,x) = x*x*x - x;
poly(4,x) = x*x*(x*x - 2.0);
poly(5,x) = x*(7.0/3 + x*x*(-10.0/3.0 + x*x));
poly(6,x) = x*x*(7.0 + x*x*(-5.0 + x*x));
p0n = float(ma.SR)/clippedFreq; // period in samples
diff1(x) = (x - x')/(2.0/p0n);
diff(N) = seq(n,N,diff1); // N diff1s in series
factorial(0) = 1;
factorial(i) = i * factorial(i-1);
D(0) = _;
D(i) = diff(i)/factorial(i+1);
gate(N) = *(1@(N)); // delayed step for blanking startup glitch
};
//------------------`(os.)sawNp`--------------------------------
// Same as `(os.)sawN` but with a controllable waveform phase.
//
// #### Usage
//
// ```
// sawNp(N,freq,phase) : _
// ```
//
// where
//
// * `N`: waveform interpolation polynomial order 1 to 4 (constant integer expression)
// * `freq`: frequency in Hz
// * `phase`: waveform phase as a fraction of one period (rounded to nearest sample)
//
// #### Implementation Notes
//
// The phase offset is implemented by delaying `sawN(N,freq)` by
// `round(phase*ma.SR/freq)` samples, for up to 8191 samples.
// The minimum sawtooth frequency that can be delayed a whole period
// is therefore `ma.SR/8191`, which is well below audibility for normal
// audio sampling rates.
//
//-----------------------------------------------------------------
declare sawNp author "Julius O. Smith III";
declare sawNp license "STK-4.3";
// --- sawNp for N = 1 to 4 ---
// Phase offset = delay (max 8191 samples is more than one period of audio):
sawNp(N,freq,phase) = sawN(N,freq) : @(max(0,min(8191,int(0.5+phase*ma.SR/freq))));
//------------------`(os.)saw2, (os.)saw3, (os.)saw4`--------------
// Alias-Suppressed Sawtooth Audio-Frequency Oscillators of order 2, 3, 4.
//
// #### Usage
//
// ```
// saw2(freq) : _
// saw3(freq) : _
// saw4(freq) : _
// ```
//
// where
//
// * `freq`: frequency in Hz
//
// ##### References
// See `sawN` above.
//
// #### Implementation Notes
//
// Presently, only `saw2` uses the PTR method, while `saw3` and `saw4` use DPW.
// This is because PTR has been implemented and tested for the 2nd-order case only.
//
//------------------------------------------------------------------
saw2 = saw2ptr; // "faustlibraries choice"
saw3 = sawN(3); // only choice available right now
saw4 = sawN(4); // only choice available right now
//---------------------------`(os.)saw2ptr`---------------------------
// Alias-Suppressed Sawtooth Audio-Frequency Oscillator
// using Polynomial Transition Regions (PTR) for order 2.
//
// #### Usage
//
// ```
// saw2ptr(freq) : _
// ```
//
// where
//
// * `freq`: frequency in Hz
//
// ##### Implementation
//
// Polynomial Transition Regions (PTR) method for aliasing suppression.
//
// ##### References
//
// * Kleimola, J.; Valimaki, V., "Reducing Aliasing from Synthetic Audio
// Signals Using Polynomial Transition Regions," in Signal Processing
// Letters, IEEE , vol.19, no.2, pp.67-70, Feb. 2012
// * <https://aaltodoc.aalto.fi/bitstream/handle/123456789/7747/publication6.pdf?sequence=9>
// * <http://research.spa.aalto.fi/publications/papers/spl-ptr/>
//
// ##### Notes
//
// Method PTR may be preferred because it requires less
// computation and is stateless which means that the frequency `freq`
// can be modulated arbitrarily fast over time without filtering
// artifacts. For this reason, `saw2` is presently defined as `saw2ptr`.
//
//--------------------------------------------------------
declare saw2ptr author "Julius O. Smith III";
declare saw2ptr license "STK-4.3";
// specialized reimplementation:
saw2ptr(freq) = y with { // newer PTR version (stateless - freq can vary at any speed)
p0 = float(ma.SR)/float(max(ma.EPSILON,abs(freq))); // period in samples
t0 = 1.0/p0; // phase increment
p = ((_<:(-(1)<:_,_),_) <: selector1,selector2) ~(+(t0)):!,_;
selector1 = select2(<(0)); // for feedback
selector2 = select2(<(0), (_<:_,(*(1-p0):+(1)):+), _); // for output
y = 2*p-1;
};
//----------------------`(os.)saw2dpw`---------------------
// Alias-Suppressed Sawtooth Audio-Frequency Oscillator
// using the Differentiated Polynomial Waveform (DWP) method.
//
// #### Usage
//
// ```
// saw2dpw(freq) : _
// ```
//
// where
//
// * `freq`: frequency in Hz
//
// This is the original Faust `saw2` function using the DPW method.
// Since `saw2` is now defined as `saw2ptr`, the DPW version
// is now available as `saw2dwp`.
//--------------------------------------------------------
declare saw2dpw author "Julius O. Smith III";
declare saw2dpw license "STK-4.3";
saw2dpw(freq) = saw1(freq) <: * <: -(mem) : *(0.25'*ma.SR/freq);
//------------------`(os.)sawtooth`--------------------------------
// Alias-suppressed aliasing-suppressed sawtooth oscillator, presently defined as `saw2`.
// `sawtooth` is a standard Faust function.
//
// #### Usage
//
// ```
// sawtooth(freq) : _
// ```
//
// with
//
// * `freq`: frequency in Hz
//--------------------------------------------------------
sawtooth = saw2; // default choice for sawtooth signal - see also sawN
//------------------`(os.)saw2f2, (os.)saw2f4`--------------------------------
// Alias-Suppressed Sawtooth Audio-Frequency Oscillator with Order 2 or 4 Droop Correction Filtering.
//
// #### Usage
//
// ```
// saw2f2(freq) : _
// saw2f4(freq) : _
// ```
//
// with
//
// * `freq`: frequency in Hz
//
// In return for aliasing suppression, there is some attenuation near half the sampling rate.
// This can be considered as beneficial, or it can be compensated with a high-frequency boost.
// The boost filter is second-order for `saw2f2` and fourth-order for `saw2f4`, and both are designed
// for the DWP case and therefore use `saw2dpw`.
// See Figure 4(b) in the DPW reference for a plot of the slight droop in the DPW case.
//--------------------------------------------------------
declare saw2f2 author "Julius O. Smith III";
declare saw2f2 license "STK-4.3";
// --- Correction-filtered versions of saw2: saw2f2, saw2f4 -----
saw2f2 = saw2dpw : cf2 with {
cf2 = fi.tf2(1.155704605878911, 0.745184288225518,0.040305967265900,
0.823765146386639, 0.117420665547108);
};
declare saw2f4 author "Julius O. Smith III";
declare saw2f4 license "STK-4.3";
saw2f4 = saw2dpw : cf4 with {
cf4 = fi.iir((1.155727435125014, 2.285861038554662,
1.430915027294021, 0.290713280893317, 0.008306401748854),
(2.156834679164532, 1.559532244409321, 0.423036498118354,
0.032080681130972));
};
//=========Alias-Suppressed Pulse, Square, and Impulse Trains============
// Alias-Suppressed Pulse, Square and Impulse Trains.
//
// `pulsetrainN`, `pulsetrain`, `squareN`, `square`, `imptrainN`, `imptrain`,
// `triangleN`, `triangle`
//
// All are zero-mean and meant to oscillate in the audio frequency range.
// Use simpler sample-rounded `lf_*` versions above for LFOs.
//
// #### Usage
//
// ```
// pulsetrainN(N,freq,duty) : _
// pulsetrain(freq, duty) : _ // = pulsetrainN(2)
//
// squareN(N,freq) : _
// square : _ // = squareN(2)
//
// imptrainN(N,freq) : _
// imptrain : _ // = imptrainN(2)
//
// triangleN(N,freq) : _
// triangle : _ // = triangleN(2)
// ```
//
// Where:
//
// * `N`: polynomial order, a constant numerical expression
// * `freq`: frequency in Hz
//====================================================================
//------------------`(os.)impulse`--------------------------------
// One-time impulse generated when the Faust process is started.
// `impulse` is a standard Faust function.
//
// #### Usage
//
// ```
// impulse : _
// ```
//--------------------------------------------------------
impulse = 1-1';
//------------------`(os.)pulsetrainN`--------------------------------
// Alias-suppressed pulse train oscillator.
//
// #### Usage
//
// ```
// pulsetrainN(N,freq,duty) : _
// ```