Will Pirkle - Designing Audio Effect Plug-Ins in C++: With Digital Audio Signal Processing Theory [2012, PDF, ENG]

Contents

Introduction .....................................................................................................xvii
Chapter 1: Digital Audio Signal Processing Principles ..............................................1
1.1 Acquisition of Samples .......................................................................................... 1
1.2 Reconstruction of the Signal .................................................................................. 3
1.3 Signal Processing Systems .................................................................................... 4
1.4 Synchronization and Interrupts .............................................................................. 5
1.5 Signal Processing Flow .......................................................................................... 6
1.6 Numerical Representation of Audio Data .............................................................. 7
1.7 Using Floating-Point Data ..................................................................................... 9
1.8 Basic DSP Test Signals ........................................................................................ 10
1.8.1 DC and Step ...................................................................................................10
1.8.2 Nyquist ...........................................................................................................11
1.8.3 ½ Nyquist .......................................................................................................11
1.8.4 ¼ Nyquist .......................................................................................................12
1.8.5 Impulse ...........................................................................................................12
1.9 Signal Processing Algorithms .............................................................................. 13
1.10 Bookkeeping ........................................................................................................ 13
1.11 The One-Sample Delay ........................................................................................ 15
1.12 Multiplication ...................................................................................................... 16
1.13 Addition and Subtraction ..................................................................................... 17
1.14 Algorithm Examples and the Difference Equation .............................................. 18
1.15 Gain, Attenuation, and Phase Inversion ............................................................... 18
1.16 Practical Mixing Algorithm ................................................................................. 19
Bibliography ................................................................................................................. 20
Chapter 2: Anatomy of a Plug-In .........................................................................21
2.1 Static and Dynamic Linking ................................................................................ 21
2.2 Virtual Address Space and DLL Access .............................................................. 22
2.3 C and C++ Style DLLs ........................................................................................ 24
2.4 Maintaining the User Interface ............................................................................ 25
2.5 The Applications Programming Interface ........................................................... 27
2.6 Typical Required API Functions .......................................................................... 29
2.7 The RackAFX Philosophy and API ..................................................................... 31
2.7.1 __stdcall .........................................................................................................31
Bibliography ............................................................................................................... 34
Chapter 3: Writing Plug-Ins with RackAFX ..........................................................35
3.1 Building the DLL ................................................................................................. 35
3.2 Creation ............................................................................................................... 36
3.3 The GUI ............................................................................................................... 36
3.4 Processing Audio ................................................................................................. 37
3.5 Destruction ........................................................................................................... 38
3.6 Your First Plug-Ins ............................................................................................... 38
3.6.1 Project: Yourplugin .........................................................................................39
3.6.2 Yourplugin GUI ..............................................................................................39
3.6.3 Yourplugin.h File ............................................................................................39
3.6.4 Yourplugin.cpp File ........................................................................................40
3.6.5 Building and Testing ......................................................................................40
3.6.6 Creating and Saving Presets ...........................................................................40
3.6.7 GUI Designer .................................................................................................40
3.7 Design a Volume Control Plug-In ........................................................................ 40
3.8 Set Up RackAFX for Use .................................................................................... 41
3.9 Setup Preferences................................................................................................. 43
3.9.1 Project: Volume ..............................................................................................44
3.9.2 Volume GUI ....................................................................................................45
3.9.3 Configure a Slider Control .............................................................................46
3.9.4 Volume.h File..................................................................................................48
3.9.5 Volume.cpp File ..............................................................................................50
3.10 Design a Volume-in-dB Plug-In........................................................................... 54
3.10.1 Project: VolumedB ........................................................................................56
3.10.2 VolumedB GUI .............................................................................................56
3.10.3 VolumedB.h File ...........................................................................................56
3.10.4 VolumedB.cpp File .......................................................................................57
3.11 Design a High-Frequency Tone Control Plug-In ................................................. 58
3.11.1 Project: SimpleHPF ......................................................................................60
3.11.2 SimpleHPF GUI ...........................................................................................60
3.11.3 SimpleHPF.h File .........................................................................................60
3.11.4 SimpleHPF.cpp File ......................................................................................62
3.12 Design a High-Frequency Tone Control with Volume Plug-In ............................ 66
3.12.1 Project: SimpleHPF ......................................................................................66
3.12.2 SimpleHPF GUI ...........................................................................................66
3.12.3 SimpleHPF.h File .........................................................................................66
3.12.4 SimpleHPF.cpp File ......................................................................................67
3.13 The User Plug-In Menu in RackAFX .................................................................. 69
Chapter 4: How DSP Filters Work ......................................................................71
4.1 First-Order Feed-Forward Filter .......................................................................... 74
4.2 Design a General First-Order Feed-Forward Filter ............................................. 84
4.3 First-Order Feed-Back Filter ............................................................................... 88
4.4 Design a General First-Order Feed-Back Filter................................................... 89
4.4.1 Project FeedBackFilter ...................................................................................89
4.4.2 FeedBackFilter GUI .......................................................................................89
4.4.3 FeedBackFilter.h File .....................................................................................89
4.4.4 FeedBackFilter.cpp File .................................................................................90
4.5 Observations ........................................................................................................ 94
4.5.1 General ...........................................................................................................94
4.5.2 Feed-Forward Filters ......................................................................................95
4.5.3 Feed-Back Filters ...........................................................................................95
Bibliography ............................................................................................................... 95
Chapter 5: Basic DSP Theory .............................................................................97
5.1 The Complex Sinusoid......................................................................................... 97
5.2 Complex Math Review ...................................................................................... 100
5.3 Time Delay as a Math Operator ......................................................................... 102
5.4 First-Order Feed-Forward Filter Revisited ........................................................ 103
5.4.1 Negative Frequencies ...................................................................................104
5.4.2 Frequencies Above and Below 6Nyquist ....................................................106
5.5 Evaluating the Transfer Function H(v) ............................................................. 106
5.5.1 DC (0 Hz) .....................................................................................................107
5.5.2 Nyquist (p) ...................................................................................................108
5.5.3 ½ Nyquist (p/2) ............................................................................................109
5.5.4 ¼ Nyquist (p/4) ............................................................................................109
5.6 Evaluating e jv ..................................................................................................... 112
5.7 The z Substitution .............................................................................................. 114
5.8 The z Transform ................................................................................................. 114
5.9 The z Transform of Signals ................................................................................ 116
5.10 The z Transform of Difference Equations .......................................................... 117
5.11 The z Transform of an Impulse Response .......................................................... 118
5.12 The Zeros of the Transfer Function ................................................................... 119
5.13 Estimating the Frequency Response: Zeros ....................................................... 121
5.14 Filter Gain Control ............................................................................................. 122
5.15 First-Order Feed-Back Filter Revisited ............................................................. 123
5.16 The Poles of the Transfer Function .................................................................... 124
5.16.1 DC (0 Hz) ...................................................................................................128
5.16.2 Nyquist (p) .................................................................................................128
5.16.3 ½ Nyquist (p/2) ..........................................................................................129
5.16.4 ¼ Nyquist (p/4) ..........................................................................................130
5.17 Second-Order Feed-Forward Filter .................................................................... 132
5.17.1 DC (0 Hz) ...................................................................................................139
5.17.2 Nyquist (p) .................................................................................................139
5.17.3 ½ Nyquist (p/2) ..........................................................................................140
5.17.4 ¼ Nyquist (p/4) ..........................................................................................140
5.18 Second-Order Feed-Back Filter ......................................................................... 142
5.18.1 DC (0 Hz) ...................................................................................................148
5.18.2 Challenge ....................................................................................................149
5.19 First-Order Pole-Zero Filter: The Shelving Filter ............................................. 149
5.19.1 DC (0 Hz) ...................................................................................................155
5.19.2 Challenge ....................................................................................................155
5.20 The Bi-Quadratic Filter ...................................................................................... 157
Bibliography ............................................................................................................... 162
Chapter 6: Audio Filter Designs: IIR Filters ........................................................163
6.1 Direct z-Plane Design ........................................................................................ 163
6.2 Single Pole Filters .............................................................................................. 164
6.2.1 First-Order LPF and HPF .............................................................................164
6.3 Resonators ......................................................................................................... 165
6.3.1 Simple Resonator .........................................................................................165
6.3.2 Smith-Angell Improved Resonator ..............................................................168
6.4 Analog Filter to Digital Filter Conversion ......................................................... 170
6.4.1 Challenge ......................................................................................................178
6.5 Effect of Poles or Zeros at Infi nity .................................................................... 178
6.6 Generic Bi-Quad Designs .................................................................................. 181
6.6.1 First-Order LPF and HPF .............................................................................182
6.6.2 Second-Order LPF and HPF ........................................................................183
6.6.3 Second-Order BPF and BSF ........................................................................184
6.6.4 Second-Order Butterworth LPF and HPF ....................................................184
6.6.5 Second-Order Butterworth BPF and BSF ....................................................185
6.6.6 Second-Order Linkwitz-Riley LPF and HPF ...............................................186
6.6.7 First- and Second-Order APF .......................................................................188
6.7 Audio Specifi c Filters ........................................................................................ 188
6.7.1 Modifi ed Bi-Quad ........................................................................................189
6.7.2 First-Order Shelving Filters .........................................................................189
6.7.3 Second-Order Parametric/Peaking Filter: Non-Constant-Q .........................191
6.7.4 Second-Order Parametric/Peaking Filter: Constant-Q .................................192
6.7.5 Cascaded Graphic EQ: Non-Constant-Q ......................................................194
6.7.6 Cascaded Graphic EQ: Constant-Q ..............................................................195
6.8 Design a Resonant LPF Plug-In ........................................................................ 196
6.8.1 Project: ResonantLPF ...................................................................................197
6.8.2 ResonantLPF GUI ........................................................................................197
6.8.3 ResonantLPF.h File ......................................................................................198
6.8.4 ResonantLPF.cpp File ..................................................................................199
6.9 The Massberg Analog-Matched Low-Pass Filter .............................................. 201
6.9.1 First-Order Massberg LPF............................................................................201
6.9.2 Second-Order Massberg LPF .......................................................................203
Bibliography ............................................................................................................. 204
References................................................................................................................. 205
Chapter 7: Delay Effects and Circular Buffers .....................................................207
7.1 The Basic Digital Delay ..................................................................................... 209
7.2 Digital Delay with Wet/Dry Mix ....................................................................... 214
7.2.1 Frequency and Impulse Responses...............................................................214
7.2.2 The Effect of Feedback ................................................................................218
7.3 Design a DDL Module Plug-In.......................................................................... 224
7.3.1 Project: DDLModule ....................................................................................225
7.3.2 DDLModule GUI .........................................................................................225
7.3.3 DDLModule.h File .......................................................................................226
7.3.4 DDLModule.cpp File ...................................................................................226
7.3.5 Declare and Initialize the Delay Line Components .....................................228
7.3.6 DDLModule.h File .......................................................................................230
7.3.7 DDLModule.cpp File ...................................................................................230
7.4 Modifying the Module to Be Used by a Parent Plug-In .................................... 233
7.4.1 DDLModule.h File .......................................................................................233
7.4.2 DDLModule.cpp File ...................................................................................234
7.5 Modifying the Module to Implement Fractional Delay ..................................... 235
7.5.1 DDLModule.cpp File ...................................................................................238
7.6 Design a Stereo Digital Delay Plug-In .............................................................. 239
7.6.1 Project: StereoDelay .....................................................................................239
7.6.2 StereoDelay GUI ..........................................................................................241
7.6.3 StereoDelay.h File ........................................................................................241
7.6.4 StereoDelay.cpp File ....................................................................................242
7.7 Design a Stereo Crossed-Feedback Delay Plug-In ............................................ 244
7.8 Enumerated Slider Variables .............................................................................. 245
7.8.1 Constructor ...................................................................................................246
7.8.2 PrepareForPlay() ..........................................................................................246
7.8.3 UserInterfaceChange() .................................................................................246
7.8.4 ProcessAudioFrame() ...................................................................................247
7.9 More Delay Algorithms ..................................................................................... 248
7.9.1 Advanced DDL Module ...............................................................................248
7.9.2 Delay with LPF in Feedback Loop ..............................................................248
7.9.3 Multi-Tap Delay ...........................................................................................249
7.9.4 Ping-Pong Delay ..........................................................................................250
7.9.5 LCR Delay ....................................................................................................250
Bibliography ............................................................................................................. 251
Chapter 8: Audio Filter Designs: FIR Filters .......................................................253
8.1 The IR Revisited: Convolution .......................................................................... 253
8.2 Using RackAFX’s Impulse Convolver .............................................................. 258
8.2.1 Loading IR Files ...........................................................................................258
8.2.2 Creating IR Files ..........................................................................................259
8.2.3 The IR File Format .......................................................................................261
8.3 Using RackAFX’s FIR Designer ....................................................................... 262
8.4 The Frequency Sampling Method...................................................................... 263
8.4.1 Linear-Phase FIR Using the Frequency Sampling Method ..........................263
8.5 Complementary Filter Design for Linear Phase FIR Filters .............................. 266
8.6 Using RackAFX’s Frequency Sampling Method Tool ...................................... 267
8.7 Designing a Complementary Filter .................................................................... 269
8.8 The Optimal (Parks-McClellan) Method ........................................................... 270
8.9 Using RackAFX’s Optimal Method Tool .......................................................... 271
8.10 Design a Convolution Plug-In ........................................................................... 273
8.10.1 Project: Convolver ......................................................................................275
8.10.2 Convolver.h File .........................................................................................275
8.10.3 Convolver.cpp File......................................................................................276
8.11 Numerical Method FIR Filters .......................................................................... 281
8.11.1 Moving Average Interpolator .....................................................................282
8.11.2 Lagrange Interpolator .................................................................................284
8.11.3 Median Filter ..............................................................................................284
Bibliography ............................................................................................................... 287
Chapter 9: Oscillators ......................................................................................289
9.1 Direct Form Oscillator ....................................................................................... 289
9.1.1 Initial Conditions ..........................................................................................290
9.2 Design a Direct Form Oscillator Plug-In ........................................................... 292
9.2.1 Project: DirectOscillator ...............................................................................292
9.2.2 DirectOscillator GUI ....................................................................................292
9.2.3 DirectOscillator.h File ..................................................................................294
9.2.4 DirectOscillator.cpp File ..............................................................................295
9.2.5 Improving the Oscillator Design ..................................................................297
9.3 The Gordon-Smith Oscillator ............................................................................ 299
9.4 Wave Table Oscillators ...................................................................................... 301
9.5 Design a Wave Table Oscillator Plug-In ............................................................ 303
9.5.1 Project: WTOscillator ...................................................................................303
9.5.2 WTOscillator GUI ........................................................................................303
9.5.3 WTOscillator.h File ......................................................................................304
9.5.4 WTOscillator.cpp File ..................................................................................305
9.6 Adding More Wave Tables ................................................................................. 308
9.6.1 WTOscillator.h File ......................................................................................308
9.6.2 WTOscillator.cpp File ..................................................................................309
9.6.3 WTOscillator GUI ........................................................................................310
9.6.4 WTOscillator.h File ......................................................................................310
9.6.5 WTOscillator.cpp File ..................................................................................311
9.7 Band-Limited Additive Wave Tables ................................................................. 312
9.7.1 WTOscillator GUI ........................................................................................313
9.7.2 WTOscillator.h File ......................................................................................313
9.7.3 WTOscillator.cpp File ..................................................................................314
9.7.4 Saw-Tooth.....................................................................................................317
9.7.5 Square Wave .................................................................................................317
9.8 Additional Oscillator Features (LFO) ................................................................ 320
9.8.1 WTOscillator.h File ......................................................................................320
9.8.2 WTOscillator.cpp File ..................................................................................321
9.8.3 WTOscillator.h File ......................................................................................321
9.8.4 WTOscillator.cpp File ..................................................................................322
9.9 Bipolar/Unipolar Functionality .......................................................................... 324
9.9.1 WTOscillator GUI ........................................................................................324
9.9.2 WTOscillator.cpp File ..................................................................................325
Bibliography ............................................................................................................. 326
Chapter 10: Modulated Delay Effects ................................................................327
10.1 The Flanger/Vibrato Effect .............................................................................. 328
10.2 The Chorus Effect ............................................................................................ 331
10.3 Design a Flanger/Vibrato/Chorus Plug-In ....................................................... 334
10.3.1 Project: ModDelayModule .........................................................................335
10.3.2 ModDelayModule GUI ..............................................................................336
10.3.3 ModDelayModule.h File ............................................................................336
10.3.4 ModDelayModule.cpp File ........................................................................337
10.3.5 PrepareForPlay() ........................................................................................340
10.3.6 Challenge ....................................................................................................342
10.4 Design a Stereo Quadrature Flanger Plug-In ................................................... 342
10.4.1 Project: StereoQuadFlanger .......................................................................342
10.4.2 StereoQuadFlanger GUI .............................................................................342
10.4.3 StereoQuadFlanger.h File ...........................................................................342
10.4.4 StereoQuadFlanger.cpp File .......................................................................343
10.4.5 Challenges ..................................................................................................345
10.5 Design a Multi-Unit LCR Chorus Plug-In ...................................................... 345
10.5.1 Project: StereoLCRChorus .........................................................................346
10.5.2 StereoLCRChorus GUI ..............................................................................346
10.5.3 StereoLCRChorus.h File ............................................................................346
10.5.4 StereoLCRChorus.cpp File ........................................................................347
10.6 More Modulated Delay Algorithms ................................................................. 350
10.6.1 Stereo Cross-Flanger/Chorus (Korg Triton®) .............................................350
10.6.2 Multi-Flanger (Sony DPS-M7®) ................................................................350
10.6.3 Bass Chorus ................................................................................................350
10.6.4 Dimension-Style (Roland Dimension D®) .................................................351
10.6.5 Deca-Chorus (Sony DPS-M7®) ..................................................................354
Bibliography ............................................................................................................. 355
Chapter 11: Reverb Algorithms .........................................................................357
11.1 Anatomy of a Room Impulse Response .......................................................... 358
11.1.1 RT60: The Reverb Time ...............................................................................359
11.2 Echoes and Modes ........................................................................................... 360
11.3 The Comb Filter Reverberator ......................................................................... 364
11.4 The Delaying All-Pass Filter Reverberator ...................................................... 368
11.5 More Delaying All-Pass Filter Reverberators .................................................. 370
11.6 Schroeder’s Reverberator ................................................................................. 372
11.7 The Low-Pass Filter–Comb Reverberator ....................................................... 373
11.8 Moorer’s Reverberator ..................................................................................... 375
11.9 Stereo Reverberation ........................................................................................ 376
11.10 Gardner’s Nested APF Reverberators .............................................................. 377
11.11 Modulated APF and Comb/APF Reverb ......................................................... 381
11.12 Dattorro’s Plate Reverb .................................................................................... 382
11.13 Generalized Feedback Delay Network Reverbs .............................................. 385
11.14 Other FDN Reverbs ......................................................................................... 389
11.15 An Example Room Reverb .............................................................................. 391
11.16 RackAFX Stock Objects .................................................................................. 394
11.16.1 COnePoleLPF ...........................................................................................394
11.16.2 CDelay ......................................................................................................395
11.16.3 CCombFilter .............................................................................................396
11.16.4 CLPFCombFilter ......................................................................................396
11.16.5 CDelayAPF ..............................................................................................398
11.17 Design the Room Reverb ................................................................................. 398
11.17.1 Project: Reverb .........................................................................................398
11.17.2 Reverb GUI ..............................................................................................398
11.17.3 Reverb.h ....................................................................................................402
11.17.4 Reverb.cpp ................................................................................................403
11.18 Challenge ......................................................................................................... 408
Bibliography ............................................................................................................... 409
References .................................................................................................................. 409
Chapter 12: Modulated Filter Effects.................................................................411
12.1 Design a Mod Filter Plug-In: Part I Modulated fc ........................................... 412
12.1.1 Project: ModFilter ......................................................................................413
12.1.2 ModFilter GUI ............................................................................................413
12.1.3 ModFilter.h File ..........................................................................................413
12.1.4 ModFilter.cpp File ......................................................................................416
12.2 Design a Mod Filter Plug-In: Part II, Modulated fc, Q .................................... 419
12.2.1 ModFilter GUI ............................................................................................419
12.2.2 ModFilter.h File ..........................................................................................419
12.2.3 ModFilter.cpp File ......................................................................................420
12.3 Design a Mod Filter Plug-In: Part III, Quad-Phase LFOs ............................... 423
12.3.1 ModFilter GUI ............................................................................................423
12.3.2 ModFilter.cpp File ......................................................................................424
12.4 Design an Envelope Follower Plug-In ............................................................. 425
12.5 Envelope Detection .......................................................................................... 428
12.5.1 Project EnvelopeFollower ..........................................................................430
12.5.2 EnvelopeFollower GUI ...............................................................................430
12.5.3 EnvelopeFollower.h File .............................................................................431
12.5.4 EnvelopeFollower.cpp File .........................................................................432
12.6 Design a Phaser Plug-In................................................................................... 436
12.6.1 Project Phaser .............................................................................................440
12.6.2 Phaser GUI .................................................................................................440
12.6.3 Phaser.h File ...............................................................................................440
12.6.4 Phaser.cpp File ...........................................................................................441
12.7 Design a Stereo Phaser with Quad-Phase LFOs .............................................. 446
12.7.1 Phaser GUI .................................................................................................446
12.7.2 Phaser.h File ...............................................................................................446
12.7.3 Phaser.cpp File ...........................................................................................447
Bibliography ............................................................................................................. 451
References................................................................................................................. 451
Chapter 13: Dynamics Processing ......................................................................453
13.1 Design a Compressor/Limiter Plug-In ............................................................. 457
13.1.1 Project: DynamicsProcessor .......................................................................458
13.1.2 DynamicsProcessor: GUI ...........................................................................458
13.1.3 DynamicsProcessor.h File ..........................................................................459
13.1.4 DynamicsProcessor.cpp File ......................................................................460
13.1.5 DynamicsProcessor.cpp File ......................................................................465
13.2 Design a Downward Expander/Gate Plug-In ................................................... 466
13.2.1 DynamicsProcessor.h File ..........................................................................466
13.2.2 DynamicsProcessor.cpp File ......................................................................466
13.3 Design a Look-Ahead Compressor Plug-In ..................................................... 468
13.3.1 DynamicsProcessor: GUI ...........................................................................469
13.3.2 DynamicsProcessor.h File ..........................................................................470
13.3.3 DynamicsProcessor.cpp File ......................................................................470
13.4 Stereo-Linking the Dynamics Processor ......................................................... 472
13.4.1 DynamicsProcessor: GUI ............................................................................472
13.4.2 DynamicsProcessor.cpp File ......................................................................473
13.5 Design a Spectral Compressor/Expander Plug-In ........................................... 475
13.5.1 Project: SpectralDynamics .........................................................................476
13.5.2 SpectralDynamics: GUI .............................................................................476
13.5.3 Additional Slider Controls ..........................................................................477
13.5.4 Spectral Dynamics Buttons ........................................................................477
13.5.5 Spectral Dynamics Metering ......................................................................477
13.5.6 SpectralDynamics.h File ............................................................................478
13.5.7 SpectralDynamics.cpp File .........................................................................479
13.6 Alternate Side-Chain Confi gurations ............................................................... 486
Bibliography ............................................................................................................. 487
References................................................................................................................. 487
Chapter 14: Miscellaneous Plug-Ins ...................................................................489
14.1 Design a Tremolo/Panning Plug-In ................................................................. 489
14.1.1 Project: TremoloPanner ..............................................................................490
14.1.2 TremoloPanner: GUI ..................................................................................490
14.2 Design a Ring Modulator Plug-In ................................................................... 494
14.2.1 Project: RingModulator ..............................................................................494
14.2.2 RingModulator: GUI ..................................................................................494
14.2.3 RingModulator.h File .................................................................................495
14.2.4 RingModulator.cpp File .............................................................................495
14.3 Design a Wave Shaper Plug-In ........................................................................ 497
14.3.1 Project: WaveShaper ...................................................................................498
14.3.2 WaveShaper: GUI .......................................................................................498
Bibliography ............................................................................................................. 500
Appendix A: The VST® and AU® Plug-In APIs .....................................................501
A.1 Compiling as a VST Plug-In in Windows ......................................................... 501
A.2 Wrapping Your RackAFX Plug-In .................................................................... 503
A.3 Comparison of Objects/Methods/GUIs ............................................................ 505
A.4 VST Plug-In without Wrapping ........................................................................ 506
A.4.1 Default GUI .................................................................................................507
A.4.2 Signal Processing ........................................................................................509
A.5 VST Plug-In with RackAFX Wrapping ............................................................ 512
A.5.1 Default GUI .................................................................................................512
A.6 AU Overview .................................................................................................... 514
A.6.1 Default GUI .................................................................................................515
A.6.2 Signal Processing ........................................................................................516
Appendix B: More RackAFX Controls and GUI Designer ......................................519
B.1 The Alpha Wheel and LCD Control .................................................................. 519
B.2 The Vector Joystick Control .............................................................................. 521
B.3 Using the sendUpdateGUI() Method ................................................................ 525
B.4 Using GUI Designer.......................................................................................... 525
Index ..............................................................................................................531