forked from grame-cncm/faustlibraries
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathhoa.lib
1079 lines (1005 loc) · 41.7 KB
/
hoa.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
//################################### hoa.lib ############################################
// Faust library for high order ambisonic. Its official prefix is `ho`.
//
// #### References
// * <https://github.com/grame-cncm/faustlibraries/blob/master/hoa.lib>
//########################################################################################
/************************************************************************
************************************************************************
FAUST library file
Copyright (C) 2003-2012 GRAME, Centre National de Creation Musicale
----------------------------------------------------------------------
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");
si = library("signals.lib");
ba = library("basics.lib");
os = library("oscillators.lib");
ho = library("hoa.lib");
declare name "High Order Ambisonics library";
declare version "0.3";
declare author "Pierre Guillot";
declare author "Eliott Paris";
declare author "Julien Colafrancesco";
declare author "Wargreen";
declare author "Alain Bonardi";
declare author "Paul Goutmann";
declare copyright "2012-2013 Guillot, Paris, Colafrancesco, CICM labex art H2H, U. Paris 8, 2019 Wargreen, 2022 Bonardi, Goutmann";
//============================Encoding/decoding Functions=================================
//========================================================================================
//----------------------`(ho.)encoder`---------------------------------
// Ambisonic encoder. Encodes a signal in the circular harmonics domain
// depending on an order of decomposition and an angle.
//
// #### Usage
//
// ```
// encoder(N, x, a) : _
// ```
//
// Where:
//
// * `N`: the ambisonic order (constant numerical expression)
// * `x`: the signal
// * `a`: the angle
//----------------------------------------------------------------
encoder(0, x, a) = x;
encoder(N, x, a) = encoder(N-1, x, a), x*sin(N*a), x*cos(N*a);
//-------`(ho.)rEncoder`----------
// Ambisonic encoder in 2D including source rotation. A mono signal is encoded at a certain ambisonic order
// with two possible modes: either rotation with an angular speed, or static with a fixed angle (when speed is zero).
//
// #### Usage
//
// ```
// _ : rEncoder(N, sp, a, it) : _,_, ...
// ```
//
// Where:
//
// * `N`: the ambisonic order (constant numerical expression)
// * `sp`: the azimuth speed expressed as angular speed (2PI/sec), positive or negative
// * `a`: the fixed azimuth when the rotation stops (sp = 0) in radians
// * `it` : interpolation time (in milliseconds) between the rotation and the fixed modes
//-----------------------------
rEncoder(N, sp, a, it) = thisEncoder
with {
basicEncoder(sig, angle) = ho.encoder(N, sig, angle);
thisEncoder = (_, rotationOrStaticAngle) : basicEncoder
with {
//converting the static angle from radians to [0; 1]
an = (a / (2 * ma.PI), 1) : fmod;
rotationOrStaticAngle = ((1-vn) * x + vn * an) * 2 * ma.PI;
//to manage the case where frequency is zero, smoothly switches from one mode to another//
vn = (sp == 0) : si.smooth(ba.tau2pole(it));
x = (os.phasor(1, sp), an, 1) : (+, _) : fmod;
};
};
//-------`(ho.)stereoEncoder`----------
// Encoding of a stereo pair of channels with symetric angles (a/2, -a/2).
//
// #### Usage
//
// ```
// _,_ : stereoEncoder(N, a) : _,_, ...
// ```
//
// Where:
//
// * `N`: the ambisonic order (constant numerical expression)
// * `a` : opening angle in radians, left channel at a/2 angle, right channel at -a/2 angle
//-----------------------------
stereoEncoder(N, a) = (leftEncoder, rightEncoder) :> si.bus(2*N+1)
with {
basicEncoder(sig, angle) = ho.encoder(N, sig, angle);
leftEncoder = (_, a / 2) : basicEncoder;
rightEncoder = (_, -a /2) : basicEncoder;
};
//-------`(ho.)multiEncoder`----------
// Encoding of a set of P signals distributed on the unit circle according to a list of P speeds and P angles.
//
// #### Usage
//
// ```
// _,_, ... : multiEncoder(N, lspeed, langle, it) : _,_, ...
// ```
//
// Where:
//
// * `N`: the ambisonic order (constant numerical expression)
// * `lspeed` : a list of P speeds in turns by second (one speed per input signal, positive or negative)
// * `langle` : a list of P angles in radians on the unit circle to localize the sources (one angle per input signal)
// * `it` : interpolation time (in milliseconds) between the rotation and the fixed modes.
//-----------------------------
multiEncoder(N, lspeed, langle, it) = par(i, P, thisEncoder(ba.take(i+1, lspeed), ba.take(i+1, langle), it)) :> si.bus(2*N+1)
with {
P = outputs(langle); //supposed to be the same as outputs(lspeed)
basicEncoder(sig, angle) = ho.encoder(N, sig, angle);
thisEncoder(sp, a, it) = (_, rotationOrStaticAngle) : basicEncoder
with {
//converting the static angle from radians to [0; 1]
an = (a / (2 * ma.PI), 1) : fmod;
rotationOrStaticAngle = ((1-vn) * x + vn * an) * 2 * ma.PI;
//to manage the case where frequency is zero, smoothly switches from one mode to another//
vn = (sp == 0) : si.smooth(ba.tau2pole(it));
x = (os.phasor(1, sp), an, 1) : (+, _) : fmod;
};
};
//--------------------------`(ho.)decoder`--------------------------------
// Decodes an ambisonics sound field for a circular array of loudspeakers.
//
// #### Usage
//
// ```
// _ : decoder(N, P) : _
// ```
//
// Where:
//
// * `N`: the ambisonic order (constant numerical expression)
// * `P`: the number of speakers (constant numerical expression)
//
// #### Note
//
// The number of loudspeakers must be greater or equal to 2n+1.
// It's preferable to use 2n+2 loudspeakers.
//-------------------------------------------------------------------
decoder(N, P) = par(i, 2*N+1, _) <: par(i, P, speaker(N, 2 * ma.PI*i/P))
with {
speaker(N,a) = /(2), par(i, 2*N, _), encoder(N, 2/P, a) : si.dot(2*N+1);
};
//-----------------------`(ho.)decoderStereo`------------------------
// Decodes an ambisonic sound field for stereophonic configuration.
// An "home made" ambisonic decoder for stereophonic restitution
// (30° - 330°): Sound field lose energy around 180°. You should
// use `inPhase` optimization with ponctual sources.
// #### Usage
//
// ```
// _ : decoderStereo(N) : _
// ```
//
// Where:
//
// * `N`: the ambisonic order (constant numerical expression)
//--------------------------------------------------------------
decoderStereo(N) = decoder(N, P) <: (par(i, 2*N+2, gainLeft(360 * i / P)) :> _),
(par(i, 2*N+2, gainRight(360 * i / P)) :> _)
with {
P = 2*N+2;
gainLeft(a) = _ * sin(ratio_minus + ratio_cortex)
with {
ratio_minus = ma.PI*.5 * abs((30 + a) / 60 * ((a <= 30)) + (a - 330) / 60 * (a >= 330));
ratio_cortex= ma.PI*.5 * abs((120 + a) / 150 * (a > 30) * (a <= 180));
};
gainRight(a) = _ * sin(ratio_minus + ratio_cortex)
with {
ratio_minus = ma.PI*.5 * abs((390 - a) / 60 * (a >= 330) + (30 - a) / 60 * (a <= 30));
ratio_cortex= ma.PI*.5 * abs((180 - a) / 150 * (a < 330) * (a >= 180));
};
};
//-------`(ho.)iBasicDecoder`----------
// The irregular basic decoder is a simple decoder that projects the incoming ambisonic situation
// to the loudspeaker situation (P loudspeakers) whatever it is, without compensation.
// When there is a strong irregularity, there can be some discontinuity in the sound field.
//
// #### Usage
//
// ```
// _,_, ... : iBasicDecoder(N,la, direct, shift) : _,_, ...
// ```
//
// Where:
//
// * `N`: the ambisonic order (there are 2*N+1 inputs to this function)
// * `la` : the list of P angles in degrees, for instance (0, 85, 182, 263) for four loudspeakers
// * `direct`: 1 for direct mode, -1 for the indirect mode (changes the rotation direction)
// * `shift` : angular shift in degrees to easily adjust angles
//-----------------------------
iBasicDecoder(N, la, direct, shift) = (par(i, 2*N+1, _) <: par(i, P, speaker(N, ang(i))))
with {
P = outputs(la);
ang(i) = (ba.take(i+1, la) - direct * shift) * direct * ma.PI / 180.;
speaker(N,alpha) = /(2), par(i, 2*N, _), ho.encoder(N,2/P,alpha) : si.dot(2*N+1);
};
//-------`(ho.)circularScaledVBAP`----------
// The function provides a circular scaled VBAP with all loudspeakers and the virtual source on the unit-circle.
//
// #### Usage
//
// ```
// _ : circularScaledVBAP(l, t) : _,_, ...
// ```
//
// Where:
//
// * `l` : the list of angles of the loudspeakers in degrees, for instance (0, 85, 182, 263) for four loudspeakers
// * `t` : the current angle of the virtual source in degrees
//-----------------------------
circularScaledVBAP(l, t) = thisCircularVbap
with {
//modulo indexes between 1 and the number of elements of the list
modIndex(i, l) = ma.modulo(i, outputs(l)) + 1;
//
//pick up the ith angle with a 360 degree modulo
getElt(i, l) = ma.modulo(ba.take(modIndex(i, l), l), 360);
//
//function to compute the sinus of the difference between angles expressed in degrees
diffSin(u, v) = sin((v - u) * ma.PI / 180.);
//
//permutations to be used to compute scaledVBAPGain
p1(a, b, c, d) = (b, c, d, a);
p2(a, b, c, d) = (a, c, b, d);
//
//computation of the scaled VBAP gain of a pair
scaledVBAPGain(t1, t2, t) = ((diffSin(t2, t) <:(_, _, _)), (ma.signum(diffSin(t2, t1)) <: (_, _)), (diffSin(t, t1) <:(_, _, _))) : (*, *, *, *) : p1 : (_, _, (+ : sqrt <: (_, _))) : p2 : (/, /);
sVBAPGain(i, l, t) = scaledVBAPGain(getElt(i, l), getElt(i+1, l), t);
//
//computes the left and the right gains using the matrix inversion (VBAP)
leftGain(i, l, t) = sVBAPGain(i, l, t) : (_, !);
rightGain(i, l, t) = sVBAPGain(i, l, t) : (!, _);
//computation of boolean activePair that determines whether the pair of LS is active or not
//we have to distinguish leftGain >0 and rightGain >= 0
//if we put >=0 for both, two pairs will be simultaneously active when theta is one of the loudspeaker angles in the list
//if we put > 0 for both, all the pairs will be inactive when theta is one of the loudspeaker angles in the list
activePair(i, l, t) = (leftGain(i, l, t) > 0) * (rightGain(i, l, t) >= 0);
//
//computes the total gain for each loudspeaker
cumulatedGain(i, l, t) = rightGain(outputs(l)+i-1, l, t) * activePair(outputs(l)+i-1, l, t) + leftGain(i, l, t) * activePair(i, l, t);
//
thisCircularVbap = _ <: par(i, outputs(l), *(cumulatedGain(i, l, t)));
};
//-------`(ho.)imlsDecoder`----------
// Irregular decoder in 2D for an irregular configuration of P loudspeakers
// using 2D VBAP for compensation.
//
// #### Usage
//
// ```
// _,_, ... : imlsDecoder(N,la, direct, shift) : _,_, ...
// ```
//
// Where:
//
// * `N`: the ambisonic order (constant numerical expression)
// * `la` : the list of P angles in degrees, for instance (0, 85, 182, 263) for four loudspeakers
// * `direct`: 1 for direct mode, -1 for the indirect mode (changes the rotation direction)
// * `shift` : angular shift in degrees to easily adjust angles
//-----------------------------
imlsDecoder(N, la, direct, shift) = si.bus(2*N+1) : iVBAPDecoder
with {
P = outputs(la);
//The VBAP decoder uses VBAP compensation: it balances the regular decoder output enabling to use irregular angular setup.
Q = max(2*N+2, P);
iVBAPDecoder = ho.decoder(N, Q) : par(i, Q, circularScaledVBAP(la, (i * 360 / Q - direct * shift) * direct)) :> si.bus(P);
};
//-------`(ho.)iDecoder`----------
// General decoder in 2D enabling an irregular multi-loudspeaker configuration
// and to switch between multi-channel and stereo.
//
// #### Usage
//
// ```
// _,_, ... : iDecoder(N, la, direct, st, g) : _,_, ...
// ```
//
// Where:
//
// * `N`: the ambisonic order (constant numerical expression)
// * `la`: the list of angles in degrees
// * `direct`: 1 for direct mode, -1 for the indirect mode (changes the rotation direction)
// * `shift` : angular shift in degrees to easily adjust angles
// * `st`: 1 for stereo, 0 for multi-loudspeaker configuration. When 1, stereo sounds goes through the first two channels
// * `g` : gain between 0 and 1
//-----------------------------
iDecoder(N, la, direct, shift, st, g) = thisDecoder
with {
//p is the number of outputs
P = outputs(la);
ambi = 1 - st;
//
//for stereo decoding
paddedStereoDecoder(N, P) = (gDecoderStereo, (0 <: si.bus(P-2)))
with {
leftDispatcher = _<:(*(1-direct), *(direct));
rightDispatcher = _<:(*(direct), *(1-direct));
gDecoderStereo = ho.decoderStereo(N) : (*(g), *(g)) : (leftDispatcher, rightDispatcher) :> (_,_);
};
//
thisDecoder = si.bus(2*N+1) <: (si.bus(2*N+1), si.bus(2*N+1)) : (imlsDecoder(N, la, direct, shift), paddedStereoDecoder(N, P)) : (par(i, P, *(ambi)), *(st), *(st), si.bus(P-2)) :> si.bus(P) : par(i, P, *(g));
};
//============================Optimization Functions======================================
// Functions to weight the circular harmonics signals depending to the
// ambisonics optimization.
// It can be `basic` for no optimization, `maxRe` or `inPhase`.
//========================================================================================
//----------------`(ho.)optimBasic`-------------------------
// The basic optimization has no effect and should be used for a perfect
// circle of loudspeakers with one listener at the perfect center loudspeakers
// array.
//
// #### Usage
//
// ```
// _ : optimBasic(N) : _
// ```
//
// Where:
//
// * `N`: the ambisonic order (constant numerical expression)
//-----------------------------------------------------
optimBasic(N) = par(i, 2*N+1, _);
//----------------`(ho.)optimMaxRe`-------------------------
// The maxRe optimization optimizes energy vector. It should be used for an
// auditory confined in the center of the loudspeakers array.
//
// #### Usage
//
// ```
// _ : optimMaxRe(N) : _
// ```
//
// Where:
//
// * `N`: the ambisonic order (constant numerical expression)
//-----------------------------------------------------
optimMaxRe(N) = par(i, 2*N+1, optim(i, N, _))
with {
optim(i, N, _)= _ * cos(indexabs / (2*N+1) * ma.PI)
with {
numberOfharmonics = 2 * N + 1;
indexabs = (int)((i - 1) / 2 + 1);
};
};
//----------------`(ho.)optimInPhase`-------------------------
// The inPhase optimization optimizes energy vector and put all loudspeakers signals
// in phase. It should be used for an auditory.
//
// #### Usage
//
// ```
// _ : optimInPhase(N) : _
// ```
//
// Where:
//
// * `N`: the ambisonic order (constant numerical expression)
//-----------------------------------------------------
optimInPhase(N) = par(i, 2*N+1, optim(i, N, _))
with {
optim(i, N, _)= _ * (fact(N)^2.) / (fact(N+indexabs) * fact(N-indexabs))
with {
indexabs = (int)((i - 1) / 2 + 1);
fact(0) = 1;
fact(n) = n * fact(n-1);
};
};
//-------`(ho.)optim`----------
// Ambisonic optimizer including the three elementary optimizers:
// `(ho).optimBasic`, `(ho).optimMaxRe` and `(ho.)optimInPhase`.
//
// #### Usage
//
// ```
// _,_, ... : optim(N, ot) : _,_, ...
// ```
//
// Where:
//
// * `N`: the ambisonic order (constant numerical expression)
// * `ot` : optimization type (0 for `optimBasic`, 1 for `optimMaxRe`, 2 for `optimInPhase`)
//-----------------------------
optim(N, ot) = thisOptimizer
with {
optb = (ot == 0) : si.smoo;
optm = (ot == 1) : si.smoo;
opti = (ot == 2) : si.smoo;
thisOptimizer = ((si.bus(2*N+1) <: ((si.bus(2*N+1):ho.optimBasic(N)), (si.bus(2*N+1):ho.optimMaxRe(N)), (si.bus(2*N+1):ho.optimInPhase(N)))), ((optb <: si.bus(2*N+1)), (optm <: si.bus(2*N+1)), (opti <: si.bus(2*N+1)))) : ro.interleave(6*N+3, 2) : par(i, 6*N+3, *) :> si.bus(2*N+1);
};
//----------------`(ho.)wider`-------------------------
// Can be used to wide the diffusion of a localized sound. The order
// depending signals are weighted and appear in a logarithmic way to
// have linear changes.
//
// #### Usage
//
// ```
// _ : wider(N,w) : _
// ```
//
// Where:
//
// * `N`: the ambisonic order (constant numerical expression)
// * `w`: the width value between 0 - 1
//-----------------------------------------------------
wider(N, w) = par(i, 2*N+1, perform(N, w, i, _))
with {
perform(N, w, i, _) = _ * (log(N+1) * (1 - w) + 1) * clipweight
with {
clipweight = weighter(N, w, i) * (weighter(N, w, i) > 0) * (weighter(N, w, i) <= 1) + (weighter(N, w, i) > 1)
with {
weighter(N, w, 0) = 1.;
weighter(N, w, i) = (((w * log(N+1)) - log(indexabs)) / (log(indexabs+1) - log(indexabs)))
with {
indexabs = (int)((i - 1) / 2 + 1);
};
};
};
};
//-------`(ho.)mirror`----------
// Mirroring effect on the sound field.
//
// #### Usage
//
// ```
// _,_, ... : mirror(N, fa) : _,_, ...
// ```
//
// Where:
//
// * `N`: the ambisonic order (constant numerical expression)
// * `fa` : mirroring type (1 = original sound field, 0 = original+mirrored sound field, -1 = mirrored sound field)
//-----------------------------
mirror(N, fa) = (*(1), par(i, N, (*(fa), *(1))));
//----------------`(ho.)map`-------------------------
// It simulates the distance of the source by applying a gain
// on the signal and a wider processing on the soundfield.
//
// #### Usage
//
// ```
// map(N, x, r, a)
// ```
//
// Where:
//
// * `N`: the ambisonic order (constant numerical expression)
// * `x`: the signal
// * `r`: the radius
// * `a`: the angle in radian
//-----------------------------------------------------
map(N, x, r, a) = encoder(N, x * volume(r), a) : wider(N, ouverture(r))
with {
volume(r) = 1. / (r * r * (r > 1) + (r <= 1));
ouverture(r) = r * (r < 1) + (r >= 1);
};
//----------------`(ho.)rotate`-------------------------
// Rotates the sound field.
//
// #### Usage
//
// ```
// _ : rotate(N, a) : _
// ```
//
// Where:
//
// * `N`: the ambisonic order (constant numerical expression)
// * `a`: the angle in radian
//-----------------------------------------------------
rotate(N, a) = par(i, 2*N+1, _) <: par(i, 2*N+1, rotation(i, a))
with {
rotation(i, a) = (par(j, 2*N+1, gain1(i, j, a)), par(j, 2*N+1, gain2(i, j, a)), par(j, 2*N+1, gain3(i, j, a)) :> _)
with {
indexabs = (int)((i - 1) / 2 + 1);
gain1(i, j, a) = _ * cos(a * indexabs) * (j == i);
gain2(i, j, a) = _ * sin(a * indexabs) * (j-1 == i) * (j != 0) * (i%2 == 1);
gain3(i, j, a) = (_ * sin(a * indexabs)) * (j+1 == i) * (j != 0) * (i%2 == 0) * (-1);
};
};
//-------`(ho.)scope`----------
// Produces an XY pair of signals representing the ambisonic sound field.
//
// #### Usage
//
// ```
// _,_, ... : scope(N, rt) : _,_
// ```
//
// Where:
//
// * `N`: the ambisonic order (constant numerical expression)
// * `rt` : refreshment time in milliseconds
//-----------------------------
scope(N, rt) = thisScope
with {
//Angle sweeping at a speed corresponding to refresh period between 0 and 2*PI
theta = os.phasor(1, 1/rt) * 2 * ma.PI;
//we get the vector of harmonic functions thanks to the encoding function//
harmonicsVector = ho.encoder(N, 1, theta);
//
normalizedVector(N) = si.bus(N) <: (si.bus(N), norm) : ro.interleave(N, 2) : par(i, N, /)
with {
norm = par(i, N, _ <:(_,_) : *) :> _ : sqrt <: ((_ == 0), (_ > 0), _) : (_,*) : + <: si.bus(N);
};
//building (2N+1) normalized vectors
inputVector = (*(0.5), par(i, (2*N), _)) : normalizedVector(2*N+1);
normalizedHarmonics = harmonicsVector : normalizedVector(2*N+1);
//
rho = (inputVector, normalizedHarmonics) : si.dot(2*N+1) ;
thisScope = (rho <: (ma.fabs, (_ >= 0))) : ((_ <: (_,_)), _) : (*(sin(theta)), *(cos(theta)), _) : (*(-1), _,_);
};
//============================Spatial Sound Processes ====================================
// We propose implementations of processes intricated to the ambisonic model.
// The process is implemented using as many instances as the number of harmonics at at certain order.
// The key control parameters of these instances are computed thanks to distribution functions
// (th functions below) and to a global driving factor.
//========================================================================================
//-------`(ho.).fxDecorrelation`----------
// Spatial ambisonic decorrelation in fx mode.
//
// `fxDecorrelation` applies decorrelations to spatial components already created.
// The decorrelation is defined for each #i spatial component among P=2\*N+1 at the ambisonic order `N`
// as a delay of 0 if factor `fa` is under a certain value 1-(i+1)/P and d\*F((i+1)/p) in the contrary case,
// where `d` is the maximum delay applied (in samples) and F is a distribution function for durations.
// The user can choose this delay time distribution among 22 different ones.
// The delay increases according to the index of ambisonic components.
// But it increases at each step and it is modulated by a threshold.
// Therefore, delays are progressively revealed when the factor increases:
//
// * when the factor is close to 0, only upper components are delayed;
// * when the factor increases, more and more components are delayed.
//
//H THRESHOLD DELAY
//0 1-1/P 0 OR DELAY*F(1/P)
//-1 1-2/P 0 OR DELAY*F(2/P)
//1 1-3/P 0 OR DELAY*F(3/P)
//-2 1-4/P 0 OR DELAY*F(4/P)
//2 1-5/P 0 OR DELAY*F(5/P)
//...
//-(N-1) 1-(P-3)/P 0 OR DELAY*F((P-3)/P)
//(N-1) 1-(P-2)/P 0 OR DELAY*F((P-2)/P)
//-N 1-(P-1)/P 0 OR DELAY*F((P-1)/P)
//N 1-P/P 0 OR DELAY*F(P/P)
//
//
// #### Usage
//
// ```
// _,_, ... : fxDecorrelation(N, d, wf, fa, fd, tf) : _,_, ...
// ```
//
// Where:
//
// * `N`: the ambisonic order (constant numerical expression)
// * `d`: the maximum delay applied (in samples)
// * `wf`: window frequency (in Hz) for the overlapped delay
// * `fa`: decorrelation factor (between 0 and 1)
// * `fd`: feedback / level of reinjection (between 0 and 1)
// * `tf`: type of function of delay distribution (integer, between 0 and 21)
//-----------------------------
fxDecorrelation(N, d, wf, fa, fd, tf) = par(i, 2*N+1, gate(d, i, 2*N+1, fa, tf, wf, fd))
with {
gate(d, i, N, fa, tf, wf, fd) = _ <: fdOverlappedDelay(dur(d, i, N, fa, tf), 262144, wf, fd) * env1(fa, i, N), _ * env1c(fa, i, N) : +;
//
fdOverlappedDelay(nsamp, nmax, freq, fdbk) = (+ : de.sdelay(nmax, int(ma.SR / freq), nsamp)) ~ (*(fdbk));
//
env1(fa, i, N) = (fa > ((N-i-1)/N)) : si.smooth(ba.tau2pole(0.005));
env1c(fa, i, N) = 1 - env1(fa, i, N);
//
//computes the ith duration of the ith delay in samples with twenty two possibilities of distribution
elemdur(d, i, p, fa, tf, ind) = (tf == ind) * (fa > (1 - x)) * d * x * fa
with {
x = th(ind, i, p);
};
//duration in samples computed as a sum of the 22 cases//
dur(d, i, p, fa, tf) = sum(ind, 22, elemdur(d, i, p, fa, tf, ind)) : int;
};
//-------`(ho.).synDecorrelation`----------
// Spatial ambisonic decorrelation in syn mode.
//
// `synDecorrelation` generates spatial decorrelated components in ambisonics from one mono signal.
// The decorrelation is defined for each #i spatial component among P=2\*N+1 at the ambisonic order `N`
// as a delay of 0 if factor `fa` is under a certain value 1-(i+1)/P and d\*F((i+1)/p) in the contrary case,
// where `d` is the maximum delay applied (in samples) and F is a distribution function for durations.
// The user can choose this delay time distribution among 22 different ones.
// The delay increases according to the index of ambisonic components.
// But it increases at each step and it is modulated by a threshold.
// Therefore, delays are progressively revealed when the factor increases:
//
// * when the factor is close to 0, only upper components are delayed;
// * when the factor increases, more and more components are delayed.
//
// When the factor is between [0; 1/P], upper harmonics are progressively faded and the level of the H0 component is compensated
// to avoid source localization and to produce a large mono.
//
//H THRESHOLD DELAY
//0 1-1/P 0 OR DELAY*F(1/P)
//-1 1-2/P 0 OR DELAY*F(2/P)
//1 1-3/P 0 OR DELAY*F(3/P)
//-2 1-4/P 0 OR DELAY*F(4/P)
//2 1-5/P 0 OR DELAY*F(5/P)
//...
//-(N-1) 1-(P-3)/P 0 OR DELAY*F((P-3)/P)
//(N-1) 1-(P-2)/P 0 OR DELAY*F((P-2)/P)
//-N 1-(P-1)/P 0 OR DELAY*F((P-1)/P)
//N 1-P/P 0 OR DELAY*F(P/P)
//
//
// #### Usage
//
// ```
// _,_, ... : synDecorrelation(N, d, wf, fa, fd, tf) : _,_, ...
// ```
//
// Where:
//
// * `N`: the ambisonic order (constant numerical expression)
// * `d`: the maximum delay applied (in samples)
// * `wf`: window frequency (in Hz) for the overlapped delay
// * `fa`: decorrelation factor (between 0 and 1)
// * `fd`: feedback / level of reinjection (between 0 and 1)
// * `tf`: type of function of delay distribution (integer, between 0 and 21)
//-----------------------------
synDecorrelation(N, d, wf, fa, fd, tf) = _ <: par(i, 2*N+1, crossFade(d, i, 2*N+1, fa, tf, wf, fd))
with {
crossFade(d, i, N, fa, tf, wf, fd) = _ <: fdOverlappedDelay(dur(d, i, N, fa, tf), 262144, wf, fd) * env1(fa, i, N), _ * env1c(fa, i, N) :> _ * env2(fa, i, N);
//
fdOverlappedDelay(nsamp, nmax, freq, fdbk) = (+ : de.sdelay(nmax, int(ma.SR / freq), nsamp)) ~ (*(fdbk));
//
env1(fa, i, N) = (fa > ((N-i-1)/N)) : si.smooth(ba.tau2pole(0.005));
env1c(fa, i, N) = 1 - env1(fa, i, N) ;
env2(fa, i, N) = ((i > 0) * N * min(fa, 1/N)) + ((i == 0) * (sqrt(N) * (1 - (N - sqrt(N)) * min(fa, 1/N)))) : si.smooth(ba.tau2pole(0.005));
//
//computes the ith duration of the ith delay in samples with twenty two possibilities of distribution
elemdur(d, i, p, fa, tf, ind) = (tf == ind) * fa * d * x
with {
x = th(ind, i, p);
};
//duration in samples computed as a sum of the 22 cases//
dur(d, i, p, fa, tf) = sum(ind, 22, elemdur(d, i, p, fa, tf, ind)) : int;
};
//-------`(ho.).fxRingMod`----------
// Spatial ring modulation in syn mode.
//
// `fxRingMod` applies ring modulation to spatial components already created.
// The ring modulation is defined for each spatial component among P=2\*n+1 at the ambisonic order `N`.
// For each spatial component #i, the result is either the original signal or a ring modulated signal
// according to a threshold that is i/P.
//
// The general process is drive by a factor `fa` between 0 and 1 and a modulation frequency `f0`.
// If `fa` is greater than theshold (P-i-1)/P, the ith ring modulator is on with carrier frequency of f0\*(i+1)/P.
// On the contrary, it provides the original signal.
//
// Therefore ring modulators are progressively revealed when `fa` increases.
//
//H THRESHOLD OUTPUT
//0 (P-1)/P ORIGINAL OR RING MODULATION BY F0*1/P
//-1 (P-2)/P ORIGINAL OR RING MODULATION BY F0*2/P
//1 (P-3)/P ORIGINAL OR RING MODULATION BY F0*3/P
//-2 (P-4)/P ORIGINAL OR RING MODULATION BY F0*4/P
//2 (P-5)/P ORIGINAL OR RING MODULATION BY F0*5/P
//...
//-(N-1) 3/P ORIGINAL OR RING MODULATION BY F0*(P-3)/P
//(N-1) 2/P ORIGINAL OR RING MODULATION BY F0*(P-2)/P
//-N 1/P ORIGINAL OR RING MODULATION BY F0*(P-1)/P
//N 0 ORIGINAL OR RING MODULATION BY F0*P/P=F0
//
//
// #### Usage
//
// ```
// _,_, ... : fxRingMod(N, f0, fa, tf) : _,_, ...
// ```
//
// Where:
//
// * `N`: the ambisonic order (constant numerical expression)
// * `f0`: the maximum delay applied (in samples)
// * `fa`: decorrelation factor (between 0 and 1)
// * `tf`: type of function of delay distribution (integer, between 0 and 21)
//-----------------------------
fxRingMod(N, f0, fa, tf) = par(i, 2*N+1, gate_ringmod(f0, i, 2*N+1, fa, tf))
with {
//
env1(fa, i, N) = (fa > ((N-i-1)/N)) : si.smooth(ba.tau2pole(0.005));
env1c(fa, i, N) = 1 - env1(fa, i, N);
//
gate_ringmod(f, i, N, fa, tf) = _ <: _ * os.osccos(freq(f, i, N, tf)) * env1(fa, i, N), _ * env1c(fa, i, N) : +;
//
ringmodfreq(f, i, N, tf, ind) = (tf == ind) * f * x * coef
with {
x = th(ind, i, N);
coef = min(1, max(N * (fa - (N - i - 1) / N), 0));
};
//
freq(f, i, N, tf) = sum(ind, 22, ringmodfreq(f, i, N, tf, ind)) : int;
};
//-------`(ho.).synRingMod`----------
// Spatial ring modulation in syn mode.
//
// `synRingMod` generates spatial components in ambisonics from one mono signal thanks to ring modulation.
// The ring modulation is defined for each spatial component among P=2\*n+1 at the ambisonic order `N`.
// For each spatial component #i, the result is either the original signal or a ring modulated signal
// according to a threshold that is i/P.
//
// The general process is drive by a factor `fa` between 0 and 1 and a modulation frequency `f0`.
// If `fa` is greater than theshold (P-i-1)/P, the ith ring modulator is on with carrier frequency of f0\*(i+1)/P.
// On the contrary, it provides the original signal.
//
// Therefore ring modulators are progressively revealed when `fa` increases.
// When the factor is between [0; 1/P], upper harmonics are progressively faded and the level of the H0 component is compensated
// to avoid source localization and to produce a large mono.
//
//H THRESHOLD OUTPUT
//0 (P-1)/P ORIGINAL OR RING MODULATION BY F0*1/P
//-1 (P-2)/P ORIGINAL OR RING MODULATION BY F0*2/P
//1 (P-3)/P ORIGINAL OR RING MODULATION BY F0*3/P
//-2 (P-4)/P ORIGINAL OR RING MODULATION BY F0*4/P
//2 (P-5)/P ORIGINAL OR RING MODULATION BY F0*5/P
//...
//-(N-1) 3/P ORIGINAL OR RING MODULATION BY F0*(P-3)/P
//(N-1) 2/P ORIGINAL OR RING MODULATION BY F0*(P-2)/P
//-N 1/P ORIGINAL OR RING MODULATION BY F0*(P-1)/P
//N 0 ORIGINAL OR RING MODULATION BY F0*P/P=F0
//
//
// #### Usage
//
// ```
// _,_, ... : synRingMod(N, f0, fa, tf) : _,_, ...
// ```
//
// Where:
//
// * `N`: the ambisonic order (constant numerical expression)
// * `f0`: the maximum delay applied (in samples)
// * `fa`: decorrelation factor (between 0 and 1)
// * `tf`: type of function of delay distribution (integer, between 0 and 21)
//-----------------------------
synRingMod(N, f0, fa, tf) = _ <: par(i, 2*N+1, crossfade_ringmod(f0, i, 2*N+1, fa, tf))
with {
//
env1(fa, i, N) = (fa > ((N-i-1)/N)) : si.smooth(ba.tau2pole(0.005));
env1c(fa, i, N) = 1 - env1(fa, i, N);
env2(fa, i, N) = ((i > 0) * N * min(fa, 1/N)) + ((i == 0) * (sqrt(N) * (1 - (N - sqrt(N)) * min(fa, 1/N)))) : si.smooth(ba.tau2pole(0.005));
//
crossfade_ringmod(f, i, N, fa, tf) = _ <: _ * os.osccos(freq(f, i, N, tf)) * env1(fa, i, N), _ * env1c(fa, i, N) :> _ * env2(fa, i, N);
//
ringmodfreq(f, i, N, tf, ind) = (tf == ind) * f * x * coef
with {
x = th(ind, i, N);
coef = min(1, max(N * (fa - (N - i - 1) / N), 0));
};
//
freq(f, i, N, tf) = sum(ind, 22, ringmodfreq(f, i, N, tf, ind)) : int;
};
//TYPES OF DISTRIBUTIONS: 22 EASING FUNCTIONS FROM [0, 1] to [0,1]
//(i+1)/p belongs to [0, 1] and its image by any function in the list also belongs to the interval
th(0, i, p) = (i+1) / p;
th(1, i, p) = ((i+1) / p)^2;
th(2, i, p) = sin(ma.PI * 0.5 * (i+1) / p);
th(3, i, p) = log10(1 + (i+1) / p) / log10(2);
th(4, i, p) = sqrt((i+1) / p);
th(5, i, p) = 1 - cos(ma.PI * 0.5 * (i+1) / p);
th(6, i, p) = (1 - cos(ma.PI * (i+1) / p)) * 0.5;
th(7, i, p) = 1 - (1 - (i+1) / p )^2;
th(8, i, p) = ((i+1) / p < 0.5) * 2 * ((i+1) / p)^2 + ((i+1) / p >= 0.5) * (1 - (-2 * (i+1) / p + 2)^2 * 0.5);
th(9, i, p) = ((i+1) / p)^3;
th(10, i, p) = 1 - (1 - (i+1) / p)^3;
th(11, i, p) = ((i+1) / p < 0.5) * 4 * ((i+1) / p)^3 + ((i+1) / p >= 0.5) * (1 - (-2 * (i+1) / p + 2)^3 * 0.5);
th(12, i, p) = ((i+1) / p)^4;
th(13, i, p) = 1 - (1 - (i+1) / p)^4;
th(14, i, p) = ((i+1) / p < 0.5) * 8 * ((i+1) / p)^4 + ((i+1) / p >= 0.5) * (1 - (-2 * (i+1) / p + 2)^4 * 0.5);
th(15, i, p) = ((i+1) / p)^5;
th(16, i, p) = 1 - (1 - (i+1) / p)^5;
th(17, i, p) = ((i+1) / p < 0.5) * 16 * ((i+1) / p)^5 + ((i+1) / p >= 0.5) * (1 - (-2 * (i+1) / p + 2)^5 * 0.5);
th(18, i, p) = 2^(10 * (i+1) / p - 10);
th(19, i, p) = ((i+1) / p < 1) * (1 - 2^(-10 * (i+1) / p)) + ((i+1) / p == 1);
th(20, i, p) = 1 - sqrt(1 - ((i+1) / p)^2);
th(21, i, p) = sqrt(1 - ((i+1) / p - 1)^2);
//========================================================================================
//============================3D Functions================================================
//========================================================================================
//========================================================================================
//----------------------`(ho.)encoder3D`---------------------------------
// Ambisonic encoder. Encodes a signal in the circular harmonics domain
// depending on an order of decomposition, an angle and an elevation.
//
// #### Usage
//
// ```
// encoder3D(N, x, a, e) : _
// ```
//
// Where:
//
// * `N`: the ambisonic order (constant numerical expression)
// * `x`: the signal
// * `a`: the angle
// * `e`: the elevation
//----------------------------------------------------------------
encoder3D(N, x, theta, phi) = par(i, (N+1) * (N+1), x * y(degree(i), order(i), theta, phi))
with {
// The degree l of the harmonic[l, m]
degree(index) = int(sqrt(index));
// The order m of the harmonic[l, m]
order(index) = int(index - int(degree(index) * int(degree(index) + 1)));
// The spherical harmonics
y(l, m, theta, phi) = e(m, theta2) * k(l, m) * p(l, m, cos(phi + ma.PI * 0.5))
with {
//theta2 enables a continuous movement of elevation (when phi becomes greater than Pi/2)
theta2 = theta + (1 - int(fmod(fmod(phi / ma.PI - 0.5, 2) + 2, 2))) * ma.PI;
//
// The associated Legendre polynomial
// If l = 0 => p = 1
// If l = m => p = -1 * (2 * (l-1) + 1) * sqrt(1 - cphi*cphi) * p(l-1, l-1, cphi)
// If l = m+1 => p = phi * (2 * (l-1) + 1) * p(l-1, l-1, cphi)
// Else => p = (cphi * (2 * (l-1) + 1) * p(l-1, abs(m), cphi) - ((l-1) + abs(m)) * p(l-2, abs(m), cphi)) / ((l-1) - abs(m) + 1)
p(l, m, cphi) = pcalcul(((l != 0) & (l == abs(m))) + ((l != 0) & (l == abs(m)+1)) * 2 + ((l != 0) & (l != abs(m)) & (l != abs(m)+1)) * 3, l, m, cphi)
with {
pcalcul(0, l, m, cphi) = 1;
pcalcul(1, l, m, cphi) = -1 * (2 * (l-1) + 1) * sqrt(1 - cphi*cphi) * p(l-1, l-1, cphi);
pcalcul(2, l, m, cphi) = cphi * (2 * (l-1) + 1) * p(l-1, l-1, cphi);
pcalcul(s, l, m, cphi) = (cphi * (2 * (l-1) + 1) * p(l-1, abs(m), cphi) - ((l-1) + abs(m)) * p(l-2, abs(m), cphi)) / ((l-1) - abs(m) + 1);
};
// The exponential imaginary
// If m > 0 => e^i*m*theta = cos(m * theta)
// If m < 0 => e^i*m*theta = sin(-m * theta)
// If m = 0 => e^i*m*theta = 1
e(m, theta) = ecalcul((m > 0) * 2 + (m < 0), m, theta)
with {
ecalcul(2, m, theta) = cos(m * theta);
ecalcul(1, m, theta) = sin(abs(m) * theta);
ecalcul(s, m, theta) = 1;
};
// The normalization
// If m = 0 => k(l, m) = 1
// If m != 0 => k(l, m) = sqrt((l - abs(m))! / l + abs(m))!) * sqrt(2)
k(l, m) = kcalcul((m != 0), l, m)
with {
kcalcul(0, l, m) = 1;
kcalcul(1, l, m) = sqrt(2) / sqrtFactQuotient(l+abs(m), l-abs(m))
with {
//factorial quotient fq(n, p)=n! / p! = n(n-1)...(p+1) when n > p
//enables factor simplification
//and considering the square root of a product as a product of square roots
sqrtFactQuotient(n, p) = sqrtProd(n-p, p)
with {
//sqrtProd(n, p) computes the product sqrt(p+1) x sqrt(p+2) x ... x sqrt(n)
//to enable factorial quotient simplification
sqrtProd(1, p) = sqrt(p+1);
sqrtProd(n, p) = sqrt(p+n) * sqrtProd(n-1, p);
};
};
};
};
};
//-------`(ho.)rEncoder3D`----------
// Ambisonic encoder in 3D including source rotation. A mono signal is encoded at at certain ambisonic order
// with two possible modes: either rotation with 2 angular speeds (azimuth and elevation), or static with a fixed pair of angles.
//
// `rEncoder3D` is a standard Faust function.
//
// #### Usage
//
// ```
// _ : rEncoder3D(N, azsp, elsp, az, el, it) : _,_, ...
// ```
//
// Where:
//
// * `N`: the ambisonic order (constant numerical expression)
// * `azsp`: the azimuth speed expressed as angular speed (2PI/sec), positive or negative
// * `elsp`: the elevation speed expressed as angular speed (2PI/sec), positive or negative
// * `az`: the fixed azimuth when the azimuth rotation stops (azsp = 0) in radians
// * `el`: the fixed elevation when the elevation rotation stops (elsp = 0) in radians
// * `it` : interpolation time (in milliseconds) between the rotation and the fixed modes
//-----------------------------
rEncoder3D(N, azsp, elsp, az, el, it) = this3DEncoder
with {
basic3DEncoder(sig, ang1, ang2) = encoder3D(N, sig, ang1, ang2);
this3DEncoder = (_, rotationOrStaticAzim, rotationOrStaticElev) : basic3DEncoder
with {
x1 = (os.phasor(1, azsp), az, 1) : (+, _) : fmod : *(2 * ma.PI);
vn1 = (azsp == 0) : si.smooth(ba.tau2pole(it));
rotationOrStaticAzim = (1-vn1) * x1 + vn1 * az;
x2 = (os.phasor(1, elsp), el, 1) : (+, _) : fmod : *(2 * ma.PI);
vn2 = (elsp == 0) : si.smooth(ba.tau2pole(it));
rotationOrStaticElev = (1-vn2) * x2 + vn2 * el;
};
};
//----------------`(ho.)optimBasic3D`-------------------------
// The basic optimization has no effect and should be used for a perfect
// sphere of loudspeakers with one listener at the perfect center loudspeakers
// array.
//
// #### Usage
//
// ```
// _ : optimBasic3D(N) : _
// ```