Designing Audio Effect Plug-Ins in C++ With Digital Audio Signal Processing Theory Will Pirkle Focal Press Taylor & Francis Croup NEW YORK AND LONDON Introduction xv Chapter 1: Digital Audio Signal Processing Principles 1.1 Acquisition of Samples 1.2 Reconstruction of the Signal 1.3 Signal Processing Systems 1.4 Synchronization and Interrupts 1.5 Signal Processing Flow 1.6 Numerical Representation of Audio Data 1.7 Using Floating-Point Data 1.8 Basic DSP Test Signals 1 1.8.1 DC and Step 1.8.2 Nyquist 1.8.3 Vi Nyquist 1.8.4 lA Nyquist 1.8.5 Impulse 1.9 Signal Processing Algorithms 1.10 Bookkeeping 1.11 The One-Sample Delay 1.12 Multiplication 1.13 Addition and Subtraction 1.14 Algorithm Examples and the Difference Equation 1.15 Gain, Attenuation, and Phase Inversion 1.16 Practical Mixing Algorithm Bibliography Chapter 2: Anatomy ofa Plug-In 2.1 Static and Dynamic Linking 2.2 Virtual Address Space and DLL Access 2.3 C and C++ Style DLLs 2.4 Maintaining the User Interface 2.5 The Applications Programming Interface 2.6 Typical Required API Functions 2.7 The RackAFX Philosophy and API 2.7.1 stdcall Bibliography VII viii Contents 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 Contents ix 4.4.1 Project FeedBackFilter 89 4.4.2 FeedBackFilter GUI 89 4.4.3 FeedBackFilter.h File 89 4.4.4 FeedBaclcFilter.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 ±Nyquist 106 5.5 Evaluating the Transfer Function H(o>) 106 5.5.1 DC(OHz) 107 5.5.2 Nyquist 0) 108 5.5.3 >/2 Nyquist (tt/2) 109 5.5.4 V* Nyquist (ir/4) 109 5.6 Evaluating 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(OHz) 128 5.16.2 Nyquist (it) 128 5.16.3 Vi Nyquist (tt/2) 129 5.16.4 Va Nyquist (ir/4) 130 5.17 Second-Order Feed-Forward Filter 132 5.17.1 DC(OHz) 139 5.17.2 Nyquist (it) 139 5.17.3 V% Nyquist (tt/2) 140 5.17.4 V* Nyquist (tt/4) 140 5.18 Second-Order Feed-B ack Filter 142 5.18.1 DC(OHz) 148 5.18.2 Challenge 149 x Contents 5.19 First-Order Pole-Zero Filter: The Shelving Filter 149 5.19.1 DC(OHz) 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 Infinity 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 Specific Filters 188 6.7.1 Modified 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 Contents xi 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 PrepareForPlayO 246 7.8.3 UserInterfaceChange() 246 7.8.4 ProcessAudioFrameQ 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 xii Contents 269 8.7 Designing a Complementary Filter 270 8.8 The Optimal (Parks-McClellan) Method 271 8.9 Using RackAFX's Optimal Method Tool 273 8.10 Design a Convolution Plug-In 275 8.10.1 Project: Convolver 275 8.10.2 Convolver.h File 276 8.10.3 Convolver.cpp File 281 8.11 Numerical Method FIR Filters 282 8.11.1 Moving Average Interpolator 284 8.11.2 Lagrange Interpolator 284 8.11.3 Median Filter 287 Bibliography 289 Chapter 9: Oscillators 289 9.1 Direct Form Oscillator 290 9.1.1 Initial Conditions 292 9.2 Design a Direct Form Oscillator Plug-In 292 9.2.1 Project: DirectOscillator 292 9.2.2 DirectOscillator GUI 294 9.2.3 DirectOscillator.h File 295 9.2.4 DirectOscillator.cpp File 297 9.2.5 Improving the Oscillator Design 299 9.3 The Gordon-Smith Oscillator 301 9.4 Wave Table Oscillators 303 9.5 Design a Wave Table Oscillator Plug-In 303 9.5.1 Project: WTOscillator 303 9.5.2 WTOscillator GUI 304 9.5.3 WTOscillator.h File 305 9.5.4 WTOscillator.cpp File 308 9.6 Adding More Wave Tables 308 9.6.1 WTOscillator.h File 309 9.6.2 WTOscillator.cpp File 310 9.6.3 WTOscillator GUI 310 9.6.4 WTOscillator.h File 311 9.6.5 WTOscillator.cpp File 312 9.7 Band-Limited Additive Wave Tables 313 9.7.1 WTOscillator GUI 313 9.7.2 WTOscillator.h File 314 9.7.3 WTOscillator.cpp File 317 9.7.4 Saw-Tooth 317 9.7.5 Square Wave 320 9.8 Additional Oscillator Features (LFO) 320 9.8.1 WTOscillator.h File 321 9.8.2 WTOscillator.cpp File 321 9.8.3 WTOscillator.h File 322 9.8.4 WTOscillator.cpp File Contents xiii 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 PrepareForPlayO 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