Real Sound Synthesis for Interactive Applications

Transcription

1 Real Sound Synthesis for Interactive Applications Perry R. Cook я А К Peters Natick, Massachusetts

2 Contents Introduction xi 1. Digital Audio Signals Introduction Digital Audio Signals Sampling and Aliasing Quantization Resampling and Interpolation Digital Audio Compression Conclusion 9 2. Sampling (Wavetable) Synthesis Introduction Wavetable Synthesis Concatenative Speech Synthesis Manipulating PCM Let's Pause and Think Here Digital Filters Introduction Linear Systems, LTI Systems, Convolution 21 # *

3 фф Contents 3.2 Digital Filters FIR Filters HR Filters The General Filter Form The Z Transform The Transfer Function Zeroes and Poles First Order One-Zero and One-Pole Filters The Second Order Pole/Zero (BiQuad) Filter A Little on Filter Topologies Conclusion Nodal Synthesis Introduction A Simple Mechanical System Solution of the Mass/Spring/Damper System Boundary Conditions and Solutions Sinusoidal Additive Synthesis Filter-Based Modal Synthesis Residual Extraction and Resynthesis Conclusion The Fourier Transform Introduction The Frequency Domain Spectrum The Fourier Series The Discrete Fourier Transform Orthogonality and Uniqueness of the DFT Convolution with the DFT and the FFT Some Fourier Transform Applications The Short-Time Fourier Transform Conclusions Spectral Modeling and Additive Synthesis Introduction Types of Spectra Spectral Modeling Sines Plus Noise Plus Transients Spectra in Time Conclusion Subband Vocoders and Filterbanks Introduction Subband Decomposition of Audio The Channel Vocoder The Cross-Synthesizing Channel Vocoder 80

4 Contents фф mi 7.4. The Phase Vocoder Conclusions Subtractive Synthesis and LPC Introduction Subtractive Synthesis Resonance-Factored (Formant) Synthesis Linear Prediction LPC Speech Examples LPC for Nonspeech and Real-World Sounds LPC and Physics Conclusions Strings and Bars Introduction The Ideal String Refining the Ideal String Weak Stiffness Really Stiff Structures: Bars Conclusions Nonlinearity, Waveshaping, FM Introduction Simple Physical Nonlinearity Simulating Physical Nonlinearity Nonlinear Wave Synthesis by Lookup Table Conclusions Tubes and Air Cavities Introduction The Ideal Acoustic Tube Building a Simple Clarinet Resonance in Air Cavities Conclusions Two and Three Dimensions Introduction Membranes and Plates, Mass/Spring Models Three-Dimensional Structures Banded Waveguides in Higher Dimensions Spatial Modes in Complex Geometries Conclusions FOFs, Wavelets, and Particles Introduction Formants in the Time Domain: FOFs 149

5 viii 4&ф Contents 13.2 Wavelets Granular Synthesis Particle Models Conclusions Exciting and Controlling Sound Models Introduction Plucking and Striking Friction Controlling Synthesis Parameters Controllers Conclusions Walking Synthesis: A Complete System Introduction Overall Architecture of the System Event Analysis Spectral Analysis Statistical Modeling and Estimation Testing on Real Sounds Parametric Resynthesis Conclusion Examples, Systems, and Applications Introduction Auditory Display: Real-Time Multimodal User Interfaces Auditory Display: Sonification Digital Foley Production Workstation/Stage Virtual and Augmented Reality Computer Music and Interactive Art Animation and Gaming The Future 209 A. DFT, Convolution, and Transform Properties 211 A.l Orthogonality of the Fourier Transform Kernel 211 A.2 Uniqueness of the Fourier Transform 212 A.3 Convolution 213 A.4 Convolution and the DFT 214 A.5 A Few Useful DFT Properties and Theorems 216 B. The Ideal String 221 B.l The Ideal String 221 С Acoustic Tubes 225 C.l The Ideal Acoustic Tube 225 C.2 D'Alembert Solution to the Acoustic Tube Equation 227

6 Contents фф C.3 Relating Pressure and Velocity in Acoustic Tubes 227 C.4 The Acoustic Tube With Varying Cross-Sectional Area 228 C.5 An Acoustic Tube Network 230 D. Sound Examples and Code on CD/CDROM 233 D.l Sound Examples 233 D.2 Source Code and Other Materials on CDROM Data Segment 236 E. TKe Synthesis Toolkit in C E.l What is the Synthesis Toolkit? 239 E.2 A Brief History of the Development of The Synthesis ToolKit 241 E.3 Synthesizing Sound in Real Time 241 E.4 Non-Real-Time Soundfile Synthesis 243 E.5 An Example Instrument: Blown Bottle 244 E.6 Real-Time Synthesis Control 245 E.7 Classes and Instruments 246 E.8 Conclusions 248 Index 249