Signals, Systems and Sound Synthesis:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Bern
Lang
2013
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXII, 595 S. graph. Darst. 1 CD |
| ISBN: | 9783034314282 3034314280 |
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| 100 | 1 | |a Neukom, Martin |d 1956- |e Verfasser |0 (DE-588)104721735X |4 aut | |
| 245 | 1 | 0 | |a Signals, Systems and Sound Synthesis |c Martin Neukom |
| 264 | 1 | |a Bern |b Lang |c 2013 | |
| 300 | |a XXII, 595 S. |b graph. Darst. |e 1 CD | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
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Datensatz im Suchindex
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| adam_text | SHORT CONTENTS
PREFACE ........... XXI
ACKNOWLEDGMENTS
......... XXIII
1 HOW TO USE THIS BOOK. ........ 1
1.1 GETTING STARTED. ........ 1
1.2 OVERVIEW. ......... 2
1.3 INSTRUCTIONS FOR USING SPECIFIC PROGRAMS . . . . .2
2 FUNDAMENTALS OF ACOUSTICS ........ 5
2.1 BASIC PHYSICAL PRINCIPLES AND UNITS ...... 5
2.2 VIBRATION AND WAVES ........ 8
2.3 SOUND AND HEARING . . . . . . . .30
3 SIGNALS AND SYSTEMS ......... 45
3.1 ANALOG SIGNALS AND THE FOURIER TRANSFORM . . . .45
3.2 DIGITAL SIGNALS, DFT,FFT 63
3.3 SYSTEMS AND FILTERS ........ 78
3.4 DYNAMIC SYSTEMS AND FEEDBACK CONTROL . . . . .109
4 COMPUTER PROGRAMS AND PROGRAMMING LANGUAGES . . . . 163
4.1 CSOUND ......... 163
4.2 MAX .......... 176
4.3 MATHEMATICA ......... 179
4.4 C/C++ 190
4.5 PROCESSING ......... 203
5 FUNDAMENTALS OF SOUND SYNTHESIS ....... 207
5.1 FUNDAMENTAL TECHNIQUES OF SOUND SYNTHESIS ..... 207
5.2 ADDITIVE SYNTHESIS ........ 244
5.3 SUBTRACTIVE SYNTHESIS ........ 259
6 NONLINEAR TECHNIQUES ........ 267
6.1 MODULATION TECHNIQUES AND DISTORTION. ..... 267
6.2 NONLINEAR SYSTEMS ........ 297
7 OTHER TECHNIQUES FOR SOUND ANALYSIS AND SYNTHESIS. . .317
7.1 GRANULAR SYNTHESIS . . . . . . .317
7.2 SPECIAL ANALYSIS METHODS ....... 328
8 PHYSICAL MODELING ......... 337
8.1 MASS-SPRING MODELS ........ 338
8.2 WAVE GUIDES. ......... 390
HTTP://D-NB.INFO/1038369657
VI
9 SOUND AND SPACE ....
9.1 SPATIAL HEARING.
9.2 REFLECTION AND REVERBERATION .
9.3 SOUND REPRODUCTION
10 COMPUTERS AND COMPOSITION .
10.1 CHANCE AND PROBABILITY
10.2 STOCHASTIC PROCESSES
10.3 OTHER TECHNIQUES USED FOR COMPOSITION
APPENDIX A FUNDAMENTALS OF MATHEMATICS .
APPENDIX B TABLES
....
BIBLIOGRAPHY .....
INDEX .....
SHORT CONTENTS
. 417
. 417
. 426
. 435
. 455
. 455
. 487
. 508
. 545
. 571
. 577
. 587
CONTENTS
PREFACE TO THE ORIGINAL GERMAN EDITION ......... XXI
PREFACE TO THE ENGLISH EDITION .......... XXII
ACKNOWLEDGEMENTS
............ XXIII
1 HOW TO USE THIS BOOK 1
1.1 GETTING STARTED ............ 1
1.2 OVERVIEW ............ 2
1.3 INSTRUCTIONS FOR USING SPECIFIC PROGRAMS ....... 2
1.3.1 USING THE MATHEMATICA NOTEBOOKS ....... 3
1.3.2 USING THE CSOUND PROGRAMS ........ 3
1.3.3 USING THE C/C++PROGRAMS 3
1.3.4 USING THE MAX PATCHES ......... 4
1.3.5 USING THE PROCESSING PROGRAMS ........ 4
2 FUNDAMENTALS OF ACOUSTICS 5
2.1 BASIC PHYSICAL PRINCIPLES AND UNITS ........ 5
2.1.1 PATH, VELOCITY, ACCELERATION ........ 5
2.1.2 MASS AND FORCE 6
2.1.3 MOMENTUM, WORK, POWER, ENERGY ....... 7
2.2 VIBRATION AND WAVES ........... 8
2.2.1 HARMONIC OSCILLATION ......... 8
2.2.1.1 DEFINITION AND MATHEMATICAL REPRESENTATION .... 8
2.2.1.2 DAMPED OSCILLATION . . . . . . .10
2.2.1.3 THE ADDITION OF HARMONIC OSCILLATIONS . . . . .11
2.2.1.4 BEATS 13
2.2.1.5 NATURAL VIBRATIONS .13
2.2.1.6 DRIVEN OSCILLATION AND RESONANCE. . . . . .15
2.2.2 PERIODIC VIBRATIONS AND THEIR SPECTRUM ...... 16
2.2.2.1 THE DEFINITION OF PERIODIC VIBRATIONS . . . . .16
2.2.2.2 STANDARD EXAMPLES . . . . . . . .16
2.2.2.3 OTHER EXAMPLES ......... 16
2.2.2.4 CONSTRUCTING PERIODIC OSCILLATION FROM HARMONIC WAVEFORMS . 17
2.2.2.5 THE SPECTRUM OF PERIODIC OSCILLATIONS . . . . .18
2.2.3 APERIODIC OSCILLATION ......... 20
2.2.3.1 NON-HARMONIC PARTIALS ........ 20
2.2.3.2 NOISE 20
2.2.3.3 PULSES 21
2.2.3.4 QUASI-PERIODIC OSCILLATION ....... 22
2.2.3.5 VARIABLE FREQUENCIES 22
2.2.4 WAVES 23
2.2.4.1 DEFINITION AND EXAMPLES ....... 23
2.2.4.2 . MATHEMATICAL DESCRIPTION ....... 24
VIII
CONTENTS
2.2.4.3 SUPERPOSITION OF WAVES ....... 25
2.2.4.4 PROPAGATION OF WAVES ........ 27
2.2.4.5 THE DOPPLER EFFECT ........ 29
2.3 SOUND AND HEARING ........... 30
2.3.1 PITCH 30
2.3.1.1 FREQUENCY RANGE AND OCTAVES ...... 30
2.3.1.2 THE HARMONIC SERIES AND PURE INTERVALS . . . . .31
2.3.1.3 INTERVALS .......... 32
2.3.2 TIMBRE ............ 33
2.3.2.1 PERIODIC VIBRATION 33
2.3.2.2 FORMANTS .......... 33
2.3.2.3 SPECTRA OF NATURAL SOUNDS ....... 34
2.3.2.4 NON-HARMONIC SPECTRA. ....... 35
2.3.2.5 FUSION .......... 36
2.3.2.6 MISSING FUNDAMENTALS AND RESIDUE PITCH .... 36
2.3.3 LOUDNESS. ........... 37
2.3.3.1 SOUND POWER AND SOUND INTENSITY ...... 37
2.3.3.2 DECIBELS .......... 37
2.3.3.3 PHONS 38
2.3.4 INTERACTION OF THE PARAMETERS . . . . . . .38
2.3.4.1 FREQUENCY GROUPS ........ 39
2.3.4.2 AUDITORY MASKING 39
2.3.4.3 COMBINATION TONES ........ 40
2.3.4.4 PARTICULAR ASPECTS OF PITCH PERCEPTION ..... 41
2.3.5 RESONANT SPACES .......... 41
2.3.5.1 REFLECTIONS AND REVERBERATION ...... 42
2.3.5.2 SOUND LOCALIZATION 43
2.3.5.3 DISTANCE PERCEPTION ........ 44
3 SIGNALS AND SYSTEMS 45
3.1 ANALOG SIGNALS AND THE FOURIER TRANSFORM ....... 45
3.1.1 PERIODIC SIGNALS AND FOURIER SERIES 46
3.1.1.1 FOURIER SERIES ......... 46
3.1.1.2 CALCULATING THE COEFFICIENTS ....... 46
3.1.1.3 EXAMPLES .......... 48
3.1.2 COMPLEX REPRESENTATION ......... 50
3.1.2.1 COMPLEX NUMBERS ........ 50
3.1.2.2 TRIGONOMETRIC REPRESENTATION . . . . .51
3.1.2.3 THE EXPONENTIAL FORM . ....... 52
3.1.2.4 ALGEBRA WITH COMPLEX NUMBERS 53
3.1.2.5 ROTATING COMPLEX VECTORS ....... 55
3.1.2.6 FOURIER ANALYSIS IN COMPLEX REPRESENTATION .... 58
3.1.3 APERIODIC SIGNALS AND FOURIER INTEGRALS ...... 60
3.1.3.1 DEFINITION .......... 60
3.1.3.2 EXAMPLES . . . . . . . . . .61
CONTENTS
IX
3.1.4 ANALOG SYSTEMS .......... 62
3.1.4.1 DEFINITION AND EXAMPLES ....... 62
3.1.4.2 LINEAR DIFFERENTIAL EQUATIONS ...... 62
3.1.4.3 LAPLACE TRANSFORM (- CD) ....... 62
3.2 DIGITAL SIGNALS, DFT, FFT 63
3.2.1 DIGITAL REPRESENTATION OF SIGNALS ....... 63
3.2.1.1 SAMPLING 63
3.2.1.2 REPRESENTATIONS AND SIMPLE EXAMPLES ..... 64
3.2.1.3 CHARACTERISTICS AND BASIC TRANSFORMATIONS .... 64
3.2.1.4 QUANTIZATION ......... 66
3.2.1.5 ALIASING .......... 66
3.2.1.6 ROTATING VECTORS 67
3.2.2 THE DISCRETE FOURIER TRANSFORM DFT ....... 68
3.2.2.1 CALCULATING THE COEFFICIENTS OF DISCRETE FOURIER SERIES . . 68
3.2.2.2 EXAMPLES .......... 68
3.2.2.3 SIGNALS WITH UNKNOWN OR NON-INTEGER PERIODS ... 69
3.2.2.4 THE COMPLEX FORM AND THE CHARACTERISTICS OF THE DFT . . 70
3.2.2.5 THE FAST FOURIER TRANSFORM FFT ...... 73
3.2.3 THE Z-TRANSFORM .......... 76
3.2.3.1 DEFINITION AND TRANSFORMATION OF SIMPLE SIGNALS ... 76
3.2.3.2 CHARACTERISTICS AND EXAMPLES ...... 77
3.3 SYSTEMS AND FILTERS ........... 78
3.3.1 SYSTEMS ............ 78
3.3.1.1 DEFINITION AND EXAMPLES . . . . .78
3.3.1.2 GENERAL PROPERTIES OF SYSTEMS . . . . . .79
3.3.1.3 IMPULSE RESPONSE AND CONVOLUTION ..... 79
3.3.1.4 PROPERTIES OF SYSTEMS IN THE FREQUENCY DOMAIN ... 80
3.3.1.5 THE COMPLEX REPRESENTATION ...... 82
3.3.1.6 FILTERS 84
3.3.1.7 THE TRANSFER FUNCTION AND THE Z-PLANE ..... 85
3.3.1.8 LINEAR PHASE FILTERS ........ 89
3.3.1.9 FILTER DESIGN ......... 90
3.3.2 NON-RECURSIVE FILTERS / FIR FILTERS 91
3.3.2.1 DEFINITIONS AND PROPERTIES . . . . . . .91
3.3.2.2 IMPLEMENTATION . . . . . . . . .91
3.3.2.3 DESIGNING FILTERS BY SETTING ZEROS 93
3.3.2.4 FOURIER APPROXIMATION. ....... 94
3.3.2.5 WINDOWING ......... 95
3.3.3 RECURSIVE FILTERS / IIR FILTERS ........ 96
3.3.3.1 DEFINITION AND PROPERTIES ....... 96
3.3.3.2 IMPLEMENTATION ......... 96
3.3.3.3 DESIGNING FILTERS BY SETTING POLES AND ZEROS .... 99
3.3.3.4 STABILITY 100
3.3.3.5 SPECIAL FILTERS ......... 100
3.3.3.6 FILTER DESIGN BY TRANSFORMING ANALOG INTO DIGITAL SYSTEMS . 108
X
CONTENTS
3.4 DYNAMIC SYSTEMS AND FEEDBACK CONTROL. . . . . . . .109
3.4.1 DIFFERENTIAL EQUATIONS . . . . . . . . .110
3.4.1.1 INTRODUCTORY EXAMPLE, PHASE SPACE . . . . .110
3.4.1.2 THE TYPES OF DIFFERENTIAL EQUATIONS AND FURTHER DEFINITIONS .
ILL
3.4.1.3 STATIONARY SYSTEM ANALYSIS, CHARACTERISTIC CURVES . . .114
3.4.1.4 NUMERICAL METHODS, DIFFERENCE EQUATIONS . . . .116
3.4.1.5 THE PENDULUM . . . . . . . . .119
3.4.2 FIXED POINTS AND ATTRACTORS 122
3.4.2.1 FIXED POINTS ......... 122
3.4.2.2 CATASTROPHES . . . . . . . . .124
3.4.2.3 ATTRACTORS. .......... 127
3.4.3 CHAOS ............ 128
3.4.3.1 INTRODUCTORY EXAMPLE . . . . . . . .128
3.4.3.2 CONDITIONS FOR CHAOS . . . . . .129
3.4.3.3 CHAOS IN TIME-DISCRETE SYSTEMS ...... 130
3.4.3.4 CHAOS IN DIFFERENTIAL EQUATIONS . . . .133
3.4.3.5 MULTIPLE SOLUTIONS AND DISCONTINUITIES . . . . .135
3.4.4 TECHNIQUES OF FEEDBACK CONTROL. ....... 137
3.4.4.1 INTRODUCTORY CONCEPTS AND EXAMPLES . . . .137
3.4.4.2 ELEMENTS OF CONTROL CIRCUITS . ...... 139
3.4.4.3 FEEDBACK CIRCUITS 144
3.4.4.4 NONLINEAR FEEDBACK CIRCUITS . ...... 145
3.4.4.5 THE COMPUTATION OF FEEDBACK CONTROL . . . .148
3.4.4.6 CONTROL BY FILTERS . . . . . . .149
3.4.4.7 EXAMPLES . . . . . . . .150
3.4.5 SYNCHRONIZATION . . . . . . . .153
3.4.5.1 SELF-SUSTAINED OSCILLATORS ....... 154
3.4.5.2 THE VAN DER POL OSCILLATOR ....... 154
3.4.5.3 SYNCHRONIZATION USING PERIODIC EXCITATION . . .156
3.4.5.4 MUTUAL SYNCHRONIZATION OF WEAKLY COUPLED OSCILLATORS . .158
3.4.5.5 SYNCHRONIZATION OF CHAOTIC OSCILLATORS . . . .160
4 COMPUTER PROGRAMS AND PROGRAMMING LANGUAGES 163
4.1 CSOUND ............ 163
4.1.1 THE SYNTAX OF THE CSOUND ORCHESTRA ....... 163
4.1 1.1
THE STRUCTURE OF THE ORCHESTRA ......
163
4.1
1.2
CONSTANTS AND VARIABLES .......
164
4.1 1.3 FUNCTIONS ..........
165
4.1 1.4 ASSIGNMENT, OPERATORS, EXPRESSIONS AND CONDITIONAL EXPRESSIONS
165
4.1 1.5
CONTROL FLOW .........
166
4.1 1.6
SIMPLE SIGNAL GENERATORS ( - CD)......
167
4.1
1.7 SIGNAL MODIFIERS ( - CD) .......
167
4.1 1.8 DELAY LINES ......... 167
4.1 1.9 SOUND INPUT AND OUTPUT 167
4.1 1.10 OPCODES
..........
168
CONTENTS
XI
4.1.2 THE SCORE ........... 168
4.1.3 FUNCTION TABLE GENERATORS . . . . . . . . .169
4.1.4 GENERATING SCORES AND EVENTS 171
4.1.4.1 GENERATING EVENTS WITH CSOUND INSTRUMENTS . . . .171
4.1.4.2 GENERATING SCORES WITH PROGRAMS IN C ..... 172
4.1.4.3 GENERATING SCORES AND EVENTS USING PROCESSING . . 173
4.1.4.4 GENERATING SCORES AND EVENTS WITH MAR .... 175
4.1.4.5 GENERATING SCORES WITH PYTHON
...... 175
4.2 MAX 176
4.2.1 FUNDAMENTALS 176
4.2.2 FEEDBACK 176
4.2.3 MXJ-OBJECTS ........... 177
4.3 MATHEMATICA ............ 179
4.3.1 FUNDAMENTALS ........... 179
4.3.2 SOUNDS . . . . . . . . . . .183
4.3.3 GRAPHICS
............ 185
4.4 C/C++ 190
4.4.1 FUNDAMENTALS . . . . . . . . .190
4.4.1.1 THE STRUCTURE OF A C PROGRAM . . . . . .190
4.4.1.2 TYPES .......... 191
4.4.1.3 DERIVED AND COMPOSITE TYPES 191
4.4.1.4 OPERATORS, EXPRESSIONS, MATHEMATICAL FUNCTIONS . . . 193
4.4.1.5 CONTROL FLOW 194
4.4.1.6 FUNCTIONS .......... 195
4.4.1.7 INPUT AND OUTPUT ........ 197
4.4.1.8 CLASSES AND OBJECTS (- CD) 199
4.4.1.9 READING AND WRITING BINARY DATA ...... 199
4.4.2 GENERATING AND STORING SOUNDS ........ 200
4.4.2.1 RAW DATA 200
4.4.2.2 SOUND FILES 201
4.5 PROCESSING ............ 203
4.5.1 FUNDAMENTALS ........... 203
4.5.2 SIMULATIONS ........... 205
4.5.3 LIBRARIES
............ 206
5 FUNDAMENTALS OF SOUND SYNTHESIS 207
5.1 FUNDAMENTAL TECHNIQUES OF SOUND SYNTHESIS ....... 207
5.1.1 OVERVIEW 207
5.1.1.1 INSTRUMENTS AND THEIR SCHEMATIC DIAGRAMS .... 207
5.1.1.2 TECHNIQUES FOR SOUND SYNTHESIS ...... 208
5.1.1.3 PROGRAMS AND PROGRAMMING LANGUAGES ..... 209
5.1.1.4 TABLES 209
5.1.1.5 AUDIO SIGNALS AND CONTROL SIGNALS. ..... 210
5.1.1.6 INTERPOLATION ......... 210
5.1.1.7 PROGRAM CONTROL AND CONDITIONAL STATEMENTS . . . .211
XII
UNIT GENERATORS .......
5.1.2.1 THE OSCILLATOR ......
5.1.2.2 THE PULSE GENERATOR .....
5.1.2.3 THE NOISE GENERATOR .....
CONTROL SIGNALS
5.1.3.1 SIMPLE CONTROL FUNCTIONS ....
5.1.3.2 SPLINES .......
5.1.3.3 INTERPOLATION FILTERS
5.1.3.4 VARIABLE CONTROL SIGNALS ....
5.1.3.5 TEMPO FUNCTIONS .....
5.1.3.6 SYNCHRONIZATION ......
DELAY LINES ........
5.1.4.1 DEFINITION AND DIRECT IMPLEMENTATION
5.1.4.2 THE CIRCULAR BUFFER
5.1.4.3 DELAY LINES WITH VARIABLE DELAY .
5.1.4.4 DELAY LINES WITH FEEDBACK ....
5.1.4.5 APPLICATIONS ......
5.2 ADDITIVE SYNTHESIS ........
5.2.1 THE SYNTHESIS OF PERIODIC WAVEFORMS .
5.2.1.1 BASIC TECHNIQUES .....
5.2.1.2 VARIABLE PARAMETERS
5.2.1.3 FUSION
5.2.1.4 DATA REDUCTION ......
5.2.1.5 ACOUSTIC ILLUSIONS .....
5.2.2 ANALYSIS-RESYNTHESIS ......
5.2.2.1 INTRODUCTION ......
5.2.2.2 THE DISCRETE FOURIER TRANSFORM DFT
5.2.2.3 LONG-TERM FOURIER TRANSFORM LTFT
5.2.2.4 SHORT-TERM FOURIER TRANSFORM STFT
5.2.2.5 THE PHASE VOCODER .....
5.3 SUBTRACTIVE SYNTHESIS ........
5.3.1 FILTERS .........
5.3.1.1 CHARACTERISTICS OF FILTERS IN THE FREQUENCY DOMAIN
5.3.1.2 TYPES OF FILTERS
5.3.1.3 SPECIAL FILTERS ......
5.3.1.4 COMBINING FILTERS .....
5.3.1.5 EFFECTS IN THE TIME DOMAIN ....
5.3.1.6 VARIABLE FILTERS ......
5.3.2 APPLICATIONS ........
5.3.2.1 SOUND SOURCES ......
5.3.2.2 RESONATORS AND FORMANTS ....
5.3.2.3 LINEAR PREDICTION. .....
6 NONLINEAR TECHNIQUES
5.1.3
CONTENTS
211
211
214
215
217
217
219
223
224
226
235
237
237
237
238
242
244
244
244
244
245
246
247
247
249
250
251
254
256
258
259
259
259
260
261
261
262
263
263
263
264
266
267
6.1 MODULATION TECHNIQUES AND DISTORTION
267
CONTENTS
6.1.1 AMPLITUDE MODULATION AND RING MODULATION
6.1.1.1 INTRODUCTORY EXAMPLE .....
6.1.1.2 BASIC TECHNIQUES .....
6.1.1.3 THE SPECTRUM OF AMPLITUDE MODULATED WAVEFORMS
6.1.2.4 RING MODULATION. .....
6.1.2 FREQUENCY MODULATION AND PHASE MODULATION
6.1.2.1 INTRODUCTORY EXAMPLE .....
6.1.2.2 THE BASIC METHOD .....
6.1.2.3 THE SPECTRUM OF A FREQUENCY MODULATED WAVEFORM
6.1.2.4 THE PROPORTION FC .FIN .....
6.1.2.5 VARIABLE SPECTRA . .....
6.1.2.6 SYNTHESIS MODELS AND EXAMPLES .
6.1.2.7 EXTENSIONS OF THE BASIC METHOD
6.1.2.8 THE INFLUENCE OF THE PHASE ....
6.1.3 NONLINEAR DISTORTION - WAVESHAPING ....
6.1.3.1 INTRODUCTORY EXAMPLES. ....
6.1.3.2 WAVESHAPING ......
6.1.3.3 THE MODULATION INDEX .....
6.1.3.4 POLYNOMIALS AS TRANSFER FUNCTIONS
6.1.3.5 CHEBYSHEV POLYNOMIALS AS TRANSFER FUNCTIONS
6.1.3.6 LIMITERS, COMPRESSORS AND EXPANDERS
6.2 NONLINEAR SYSTEMS
6.2.1 NON-RECURSIVE SYSTEMS WITH A SINGLE INPUT.
6.2.1.1 FUNCTIONS OF A SINGLE INPUT VALUE .
6.2.1.2 FUNCTIONS OF MORE THAN ONE INPUT VALUE
6.2.2 NON-RECURSIVE SYSTEMS WITH MORE THAN ONE INPUT SIGNAL
6.2.2.1 FUNCTIONS USING A SINGLE VALUE OF EACH INPUT.
6.2.2.2 SPECIAL FUNCTIONS OF TWO INPUT SIGNALS .
6.2.2.3 FUNCTIONS OF SEVERAL VALUES OF SEVERAL INPUT SIGNALS
6.2.3 RECURSIVE SYSTEMS .......
6.2.3.1 FUNCTIONS OF ONE VALUE ....
6.2.3.2 FUNCTIONS OF TWO VALUES ....
6.2.4 TIME-VARIANT SYSTEMS ......
6.2.4.1 DELIMITING SYSTEMS .....
6.2.4.2 NON-RECURSIVE SYSTEMS WITH CONSTANT DELAY .
6.2.4.3 NON-RECURSIVE SYSTEMS WITH VARIABLE DELAY .
6.2.4.4 RECURSIVE SYSTEMS WITH CONSTANT DELAY.
6.2.4.5 RECURSIVE SYSTEMS WITH VARIABLE DELAY .
7 OTHER TECHNIQUES FOR SOUND ANALYSIS AND SYNTHESIS
7.1 GRANULAR SYNTHESIS ........
7.1.1 FUNDAMENTALS ........
7.1.1.1 GRAINS .......
7.1.1.2 TECHNIQUES FOR MAKING AND CONTROLLING GRAINS
7.1.1.3 SYNCHRONOUS GRANULAR SYNTHESIS
XIV
7.1.1.4 ASYNCHRONOUS GRANULAR SYNTHESIS .
7.1.2
APPLICATIONS
.........
7.1.2.1 FOF
7.1.2.2 VOSIM
7.1.2.3 GRANULATING SAMPLED SOUNDS ....
7.2
SPECIAL
ANALYSIS
METHODS
........
7.2.1 WALSH SYNTHESIS ........
7.2.1.1 WALSH FUNCTIONS . ......
7.2.1.2 EXAMPLES ........
7.2.2 THE LOGARITHMIC FREQUENCY RANGE IN SPECTRAL ANALYSIS .
7.2.3 WAVELETS. .........
7.2.3.1 WAVELETS
7.2.3.2 THE CONTINUOUS WAVELET TRANSFORM
7.2.3.3 THE DISCRETE WAVELET TRANSFORM ....
8 PHYSICAL MODELING
8.1 MASS-SPRING MODELS .........
8.1.1 SYSTEMS WITH ONE MASS .......
8.1.1.1 HARMONIC OSCILLATION
8.1.1.2 EXCITING THE OSCILLATION .....
8.1.1.3 DAMPED HARMONIC OSCILLATION ....
8.1.1.4 EXCITING THE DAMPED OSCILLATION ....
8.1.1.5 OSCILLATION WITH NONLINEAR ACCELERATION .
8.1.1.6 CALCULATIONS .......
8.1.2 SYSTEMS WITH TWO MASSES. ......
8.1.2.1 THE OSCILLATION OF TWO COUPLED MASSES .
8.1.2.2 EXCITATION AND DAMPING .....
8.1.2.3 NONLINEAR ACCELERATION
8.1.2.4 COMPUTING THE FREQUENCIES OF THE NATURAL RESONANCES
8.1.2.5 CALCULATIONS (- CD) ......
8.1.3 THE LINEAR ARRANGEMENT OF COUPLED MASSES.
8.1.3.1 A MODEL WITH THREE MASSES. ....
8.1.3.2 THE STRING
8.1.3.3 CORRECTING THE DISPERSION RELATION.
8.1.3.4 DAMPING AND NONLINEARITY .....
8.1.3.5 PICKING UP THE SOUND
8.1.3.6 EXCITING THE STRING ......
8.1.3.7 HARMONICS ........
8.1.4 TWO-DIMENSIONAL ARRANGEMENTS OF COUPLED MASSES
8.1.4.1 AN EXAMPLE WITH THREE MASSES ....
8.1.4.2 REPRESENTING THE PLANE BY A REGULAR GRID
8.1.4.3 RESONANT FREQUENCIES OF THE GRID ....
8.1.4.4 OBJECTS WITH CURVED EDGES .....
8.1.4.5 OBJECTS WITH FREELY OSCILLATING EDGES
8.1.4.6 RIGID BODY MOTION ......
CONTENTS
322
323
323
324
326
328
328
329
329
330
331
331
332
335
337
338
338
338
342
342
345
347
348
349
349
351
352
353
355
355
355
356
358
360
361
362
363
365
365
366
367
369
369
370
CONTENTS
8.1.4.7 RETROFLEX SURFACES . . . . . . . .371
8.1.4.8 A GRID WITH UNEQUAL DISTANCES BETWEEN THE MASSES . . 372
8.1.4.9 IRREGULAR GRIDS 374
8.1.4.10 IRREGULAR DENSITY OR ELASTICITY ...... 376
8.1.5 THREE-DIMENSIONAL ARRANGEMENTS OF COUPLED MASSES .... 377
8.1.5.1 LONGITUDINAL AND TRANSVERSAL OSCILLATIONS OF A MASS. . . 377
8.1.5.2 SUBDIVIDING SPACE WITH A REGULAR GRID . .... 378
8.1.5.3 BODIES IN FREE MOTION
........ 380
8.1.5.4 A MODEL WITH FIXED POINTS ....... 383
8.1.5.5 VARIABLE FIXED POINTS ........ 385
8.1.5.6 THE EFFECT OF GRAVITY ........ 386
8.1.5.7 DAMPING .......... 386
8.1.6 ARBITRARY CONFIGURATIONS AND VARIATIONS 387
8.1.6.1 COUPLED STRINGS ......... 387
8.1.6.2 GEOMETRICALLY IMPOSSIBLE SHAPES ...... 388
8.1.6.3 SPACES OF MORE THAN THREE DIMENSIONS . .... 389
8.2 WAVE GUIDES. ............ 390
8.2.1 SIMPLE DELAY LINES .......... 390
8.2.1.1 DELAY LINES ......... 390
8.2.1.2 SIMPLE DAMPING. ........ 392
8.2.1.3 FREQUENCY .......... 393
8.2.1.4 NONLINEARITY 396
8.2.1.5 THE EXCITATION ......... 397
8.2.1.6 THE KARPLUS-STRONG ALGORITHM ...... 398
8.2.2 WAVEGUIDES ........... 399
8.2.2.1 THE IDEAL WAVEGUIDE ........ 400
8.2.2.2 REFLECTION .......... 401
8.2.2.3 THE ADVANCING WAVE FRONT AS SOLUTION OF THE WAVE EQUATION . 402
8.2.2.4 OTHER VARIABLES FOR REPRESENTING WAVES. .... 404
8.2.3. SOUND PICKUP AND EXCITATION ........ 405
8.2.3.1 THE POSTIONS OF PICKUP AND EXCITATION ..... 405
8.2.3.2 THE DURATION OF THE EXCITATION ...... 407
8.2.3.3 EXCITATION WITHOUT FEEDBACK ...... 408
8.2.3.4 EXCITATION WITH FEEDBACK ....... 410
8.2.3.5 SELECTIVE REFLECTION AND SOUND RADIATION . . .413
8.2.3.6 HARMONICS 414
9 SOUND AND SPACE 417
9.1 SPATIAL HEARING ............ 417
9.1.1 SOUND LOCALIZATION .......... 418
9.1.1.1 INTERAURAL TIME DIFFERENCE ITD . . , . . .418
9.1.1.2 INTERAURAL INTENSITY DIFFERENCE IID. . . . . .419
9.1.1.3 HEAD-RELATED TRANSFER FUNCTION HRTF ..... 421
9.1.2 DISTANCE ............ 422
9.1.2.1 THE DECREASE OF SOUND INTENSITY WITH DISTANCE . . . 422
XVI
CONTENTS
9.1.2.2 PROPORTION OF INDIRECT SOUND . ...... 423
9.1.3 MOVEMENT OF SOUND IN SPACE ........ 424
9.1.3.1 THE DOPPLER EFFECT 424
9.1.3.2 ADDITIONAL INFORMATION THROUGH POSITION CHANGE . . . 425
9.2 REFLECTION AND REVERBERATION ......... 426
9.2.1 REFLECTIONS ........... 426
9.2.1.1 GEOMETRICAL CONSIDERATIONS ....... 426
9.2.1.2 SCATTER AND ABSORBTION. ....... 430
9.2.2 REVERBERATION ........... 430
9.2.2.1 THE NATURE OF REVERBERATION. . . . . . .431
9.2.2.2 SIMPLE REVERBERATORS . . . . . . . .431
9.2.2.3 FREQUENCY DEPENDENCY ....... 434
9.2.2.4 MORE COMPLEX FILTERS ........ 435
9.2.2.5 CONVOLUTION WITH AN IMPULSE RESPONSE ..... 435
9.3 SOUND REPRODUCTION ........... 435
9.3.1 IDEAL SOLUTIONS. .......... 435
9.3.1.1 SIMULATION OF THE SOUND SOURCE ...... 436
9.3.1.2 SOUND FIELD REPRODUCTION ....... 436
9.3.1.3 THE SOUND WAVE IN THE AUDITORY CANAL ..... 437
9.3.2 PRACTICAL SOLUTIONS .......... 437
9.3.2.1 STEREO 438
9.3.2.2 AMBISONICS ......... 438
9.3.2.3 DECORRELATION . . . . . . . . .451
10 COMPUTERS AND COMPOSITION 455
10.1 CHANCE AND PROBABILITY .......... 455
10.1.1 FUNDAMENTALS OF COMBINATORICS ........ 455
10.1.1.1 INTRODUCTORY EXAMPLES. ....... 455
10.1.1.2 PERMUTATIONS ......... 456
10.1.1.3 COMBINATIONS ......... 456
10.1.1.4 ARRANGEMENTS ......... 457
10.1.1.5 ORDERING PERMUTATIONS 458
10.1.1.6 BINOMIAL AND POLYNOMIAL COEFFICIENTS . . . .458
10.1.2 FUNDAMENTALS OF PROBABILITY CALCULUS . ...... 458
10.1.2.1 STANDARD EXAMPLES AND DEFINITIONS ..... 458
10.1.2.2 COMBINING EVENTS ........ 459
10.1.2.3 THE TERMINOLOGY AND AXIOMS OF PROBABILITY THEORY. . 459
10.1.2.4 CONDITIONAL PROBABILITY AND STOCHASTIC INDEPENDENCE . . 461
10.1.2.5 EXAMPLES .......... 461
10.1.3 PROBABILITY, DENSITY AND DISTRIBUTION FUNCTIONS OF RANDOM
VARIABLES . 461
10.1.3.1 RANDOM VARIABLES AND THE PROBABILITY FUNCTION . . 462
10.1.3.2 CONTINUOUS RANDOM VARIABLES AND THEIR DENSITY FUNCTION . 462
10.1.3.3 DISTRIBUTION FUNCTIONS ........ 463
10.1.3.4 CONTINUOUS DENSITY FUNCTIONS AND THEIR DISTRIBUTIONS . 464
10.1.3.5 FUNCTIONS OF RANDOM VARIABLES ...... 465
CONTENTS XVII
10.1.3.6 MEASURING PROBABILITY DISTRIBUTION ..... 465
10.1.3.7 PARAMETRIC CONTROL OF FUNCTIONS ...... 467
10.1.4 GENERATING RANDOM NUMBERS WITH A GIVEN DENSITY OR DISTRIBUTION. .
467
10.1.4.1 PSEUDORANDOM NUMBERS ....... 467
10.1.4.2 DIRECT METHODS FOR GENERATING A GIVEN DISTRIBUTION . . . 469
10.1.4.3 INVERTING THE DISTRIBUTION FUNCTION ..... 470
10.1.4.4 REJECTION SAMPLING ........ 472
10.1.4.5 TABLES OF ELEMENTS WITH SPECIFIED FREQUENCY OF OCCURRENCE . 473
10.1.5 PARTICULAR DISTRIBUTIONS ......... 476
10.1.5.1 CONTINUOUS UNIFORM DISTRIBUTION . . . . . .476
10.1.5.2 TRAPEZOID DISTRIBUTION . ....... 476
10.1.5.3 BINOMIAL DISTRIBUTION ........ 477
10.1.5.4 POISSON DISTRIBUTION ........ 478
10.1.5.5 NORMAL DISTRIBUTION ........ 479
10.1.5.6 EXPONENTIAL DISTRIBUTION ....... 480
10.1.5.7 GAMMA DISTRIBUTION ........ 481
10.1.5.8 WEIBULL DISTRIBUTION . . . . . . .481
10.1.6 APPLICATIONS ........... 483
10.1.6.1 SOUND EXAMPLES FROM RANDOM NUMBER SEQUENCES . 483
10.1.6.2 THE APPLICATION OF RANDOM NUMBERS TO MUSICAL PARAMETERS . 484
10.1.6.3 APPLICATIONS USING VARIABLE DISTRIBUTIONS .... 485
10.1.6.4 CHOOSING AMONG RANDOM VALUES . ..... 487
10.2 STOCHASTIC PROCESSES ........... 487
10.2.1 INTRODUCTORY EXAMPLES AND CONCEPTS 487
10.2.1.1 GAMES OF CHANCE ........ 487
10.2.1.2 WHITE NOISE 488
10.2.1.3 GENERAL FORMULATION OF THE CONCEPTS ..... 489
10.2.2 MARKOV CHAINS .......... 490
10.2.2.1 INTRODUCTORY EXAMPLES. ....... 490
10.2.2.2 DEFINITION 492
10.2.2.3 TRANSITION MATRIX AND STATE VECTORS ..... 493
10.2.2.4 APPLICATIONS ......... 494
10.2.2.5 MARKOV CHAINS WITH VARIABLE TRANSITION PROBABILITIES . . 497
10.2.2.6 MARKOV CHAINS WITH VARIABLE STATES ..... 499
10.2.2.7 OTHER EXAMPLES ......... 499
10.2.3 MORE STOCHASTIC PROCESSES ........ 502
10.2.3.1 PROCESSES WITH INDEPENDENT INCREMENTS . .... 502
10.2.3.2 RANDOM WALK ......... 503
10.2.3.3 DESCRIBING A PROCESS BY ITS SPECTRUM ..... 505
10.2.3.4 PROCESSES INVOLVING PREVIOUS EVENTS ..... 506
10.2.3.5 PROCESSES WITH SIEVED RANDOM VARIABLES .... 507
10.3 OTHER TECHNIQUES USED FOR COMPOSITION. ....... 508
10.3.1 CELLULAR AUTOMATA .......... 508
10.3.1.1 ONE-DIMENSIONAL AUTOMATA WITH TWO STATES .... 508
10.3.1.2 ONE-DIMENSIONAL AUTOMATA WITH MANY STATES . . .510
XVIII
CONTENTS
10.3.1.3 TWO-DIMENSIONAL AUTOMATA WITH TWO STATES . . 513
10.3.2 THE GOLDEN RATIO .......... 514
10.3.2.1 DEFINITION AND CLASSICAL CONSTRUCTION . . . . .515
10.3.2.2 FIBONACCI NUMBERS ........ 516
10.3.2.3 CONTINUED FRACTIONS, SURDS AND GOLDEN RATIO . . .516
10.3.2.4 FRACTALS ... 518
10.3.2.5 A PROCESS OF NATURAL GROWTH. ...... 518
10.3.2.6 APPLICATIONS ......... 520
10.3.3 CHAOS THEORY ........... 525
10.3.3.1 CONCEPTS .......... 525
10.3.3.2 THE THEORY OF DYNAMIC SYSTEMS ...... 526
10.3.3.3 SELF-SIMILARITY AND FRACTALS ....... 527
10.3.3.4 APPLICATIONS TO MUSIC ........ 528
10.3.4 SIMULATING SWARM BEHAVIOR ........ 531
10.3.4.1 THE CLASSICAL BOIDS ALGORITHM ...... 531
10.3.4.2 EXTENSIONS OF THE SWARM ALGORITHM 533
10.3.4.3 IMPLEMENTATIONS . . . . . . .533
10.3.5 TOWARD A TOPOLOGY OF SOUNDS ........ 535
10.3.5.1 MENTAL REPRESENTATION . ....... 535
10.3.5.2 COMPLEX TOPOLOGIES TO REPRESENT PITCH SPACE. . . . 537
10.3.5.3 TIME 539
10.3.5.4 TIMBRE 540
10.3.5.5 POSITION SPACE ......... 541
10.3.5.6 MAPPING .......... 542
10.3.5.7 SYSTEMS .......... 543
APPENDIX A FUNDAMENTALS OF MATHEMATICS 545
A.L NUMBERS
AND
ARITHMETIC
OPERATIONS ........ 545
A.1.1 NUMBERS. ........... 545
A.1.2 RULES OF ALGEBRA .......... 545
A.2 STATEMENTS, SETS AND OPERATIONS ON SETS 546
A.2.1 STATEMENTS ........... 546
A.2.2 SETS 547
A.2.3 SUBSETS AND POWER SET ......... 547
A.2.4 OPERATIONS ON SETS 547
A.2.5 THE CARTESIAN PRODUCT ......... 547
A.3 EQUATIONS ............ 548
A.3.1 DEFINITIONS AND CONCEPTS ......... 548
A.3.2 EQUIVALENCE TRANSFORMATIONS ........ 548
A.3.3 ALGEBRAIC EQUATIONS .......... 548
A.3.4 SYSTEMS OF LINEAR EQUATIONS AND MATRICES ...... 549
A.3.5 TRANSCENDENTAL EQUATIONS ......... 550
A.4 FUNCTIONS 551
A.4.1 DEFINITION ........... 551
CONTENTS XIX
A.4.2 PROPERTIES OF FUNCTIONS AND GRAPHICAL REPRESENTATION .... 552
A.4.3 BASIC FUNCTIONS .......... 553
A.4.4 COMPOSITE FUNCTIONS 562
A.4.5 PARAMETRIC REPRESENTATION ......... 562
A.4.6 FUNCTIONS OF SEVERAL VARIABLES 563
A.4.7 EVEN AND ODD FUNCTIONS ......... 564
A.4.8 SEQUENCES AND SERIES 564
A.5 CALCULUS ............ 565
A.5.1 THE DERIVATIVE OF A FUNCTION ........ 565
A.5.2 RULES FOR DIFFERENTIATION ......... 566
A.5.3 THE INDEFINITE INTEGRAL OF A FUNCTION ....... 567
A.5.4 INTEGRATION FORMULAS 567
A.5.5 THE DEFINITE INTEGRAL. ......... 568
A.5.6 PARTIAL DERIVATIVES .......... 568
APPENDIX B TABLES 571
B.L PITCHES . 571
B.2 FORMANTS OF ENGLISH VOWELS . . . . . . . . .571
B.3 CONSTANTS ............ 572
B.4 FIBONACCI NUMBERS 572
B.5 PRIME NUMBERS ............ 573
B.6 BESSEL FUNCTIONS ............ 574
B.7 CHEBYSHEV POLYNOMIALS . . . . . . . . . .575
BIBLIOGRAPHY 577
BOOKS (BY AUTHOR) ........... 577
BOOKS (BY NUMBER OF REFERENCE) ......... 580
ARTICLES FROM THE COMPUTER MUSIC JOURNAL (CMJ) 584
ARTICLES FROM OTHER SOURCES .......... 585
ARTICLES AVAILABLE ON THE INTERNET 586
INDEX
587
|
| any_adam_object | 1 |
| author | Neukom, Martin 1956- |
| author_GND | (DE-588)104721735X |
| author_facet | Neukom, Martin 1956- |
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| dewey-ones | 780 - Music |
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| dewey-search | 780.285 |
| dewey-sort | 3780.285 |
| dewey-tens | 780 - Music |
| discipline | Musikwissenschaft |
| format | Book |
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| id | DE-604.BV041268648 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:43:37Z |
| institution | BVB |
| isbn | 9783034314282 3034314280 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026242297 |
| oclc_num | 858839953 |
| open_access_boolean | |
| owner | DE-11 |
| owner_facet | DE-11 |
| physical | XXII, 595 S. graph. Darst. 1 CD |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Lang |
| record_format | marc |
| spelling | Neukom, Martin 1956- Verfasser (DE-588)104721735X aut Signals, Systems and Sound Synthesis Martin Neukom Bern Lang 2013 XXII, 595 S. graph. Darst. 1 CD txt rdacontent n rdamedia nc rdacarrier Computermusik (DE-588)4113239-7 gnd rswk-swf Soundverarbeitung (DE-588)4485311-7 gnd rswk-swf Soundverarbeitung (DE-588)4485311-7 s Computermusik (DE-588)4113239-7 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026242297&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Neukom, Martin 1956- Signals, Systems and Sound Synthesis Computermusik (DE-588)4113239-7 gnd Soundverarbeitung (DE-588)4485311-7 gnd |
| subject_GND | (DE-588)4113239-7 (DE-588)4485311-7 |
| title | Signals, Systems and Sound Synthesis |
| title_auth | Signals, Systems and Sound Synthesis |
| title_exact_search | Signals, Systems and Sound Synthesis |
| title_full | Signals, Systems and Sound Synthesis Martin Neukom |
| title_fullStr | Signals, Systems and Sound Synthesis Martin Neukom |
| title_full_unstemmed | Signals, Systems and Sound Synthesis Martin Neukom |
| title_short | Signals, Systems and Sound Synthesis |
| title_sort | signals systems and sound synthesis |
| topic | Computermusik (DE-588)4113239-7 gnd Soundverarbeitung (DE-588)4485311-7 gnd |
| topic_facet | Computermusik Soundverarbeitung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026242297&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT neukommartin signalssystemsandsoundsynthesis |