Introduction to Sound Processing

Sound manipulation is an activity that find an increasing number of practitioners in the fields of artistic expression, technology, and science. These people have different goals and different backgrounds, but they greatly benefit from talking to each other using a common language and common tools. This book is aimed at providing such language and mathematical, algorithmic, and computational tools. Continuous-Time Systems......Page 9 The Sampling Theorem......Page 11 Discrete-Time Spectral Representations......Page 14 Discrete-Time Systems......Page 19 The Impulse Response......Page 20 The Shift Theorem......Page 21 Stability and Causality......Page 22 Impulse Invariance......Page 23 Bilinear Transformation......Page 25 Quantization......Page 27 Digital Filters......Page 31 The Simplest FIR Filter......Page 32 The Phase Response......Page 37 Higher-Order FIR Filters......Page 40 Realizations of FIR Filters......Page 48 The Simplest IIR Filter......Page 51 Higher-Order IIR Filters......Page 55 Allpass Filters......Page 63 Realizations of IIR Filters......Page 65 Complementary filters and filterbanks......Page 70 Frequency warping......Page 72 The Circular Buffer......Page 75 Fractional-Length Delay Lines......Page 76 FIR Interpolation Filters......Page 77 Allpass Interpolation Filters......Page 80 The Non-Recursive Comb Filter......Page 82 The Recursive Comb Filter......Page 84 The Comb-Allpass Filter......Page 86 Sound Effects Based on Delay Lines......Page 87 Spatialization......Page 89 Reverberation......Page 97 The Filterbank View......Page 107 The DFT View......Page 108 Windowing......Page 111 Representations......Page 116 Accurate partial estimation......Page 118 Linear predictive coding (with Federico Fontana)......Page 121 The sinusoidal model......Page 125 Sines + Noise + Transients......Page 130 LPC Modelling......Page 131 The Digital Oscillator......Page 132 The Wavetable Oscillator......Page 133 Wavetable sampling synthesis......Page 135 Granular synthesis (with Giovanni De Poli)......Page 137 Frequency and phase modulation......Page 138 Nonlinear distortion......Page 143 A physical oscillator......Page 145 Coupled oscillators......Page 146 One-dimensional distributed resonators......Page 149 Fields......Page 153 Rings......Page 154 Complex Numbers......Page 155 Variables and Functions......Page 156 Polynomials......Page 160 Vectors and Matrices......Page 162 Exponentials and Logarithms......Page 166 Trigonometric Functions......Page 169 Derivatives of Functions......Page 172 Integrals of Functions......Page 176 Transforms......Page 177 The Laplace Transform......Page 178 The Fourier Transform......Page 179 The Z Transform......Page 180 Integer Numbers......Page 181 Rational Numbers......Page 183 Tools for Sound Processing (with Nicola Bernardini)......Page 185 Sounds in Matlab and Octave......Page 186 Digression......Page 187 Languages for Sound Processing......Page 190 Unit generator......Page 193 Examples in Csound, SAOL, and CLM......Page 194 Interactive Graphical Building Environments......Page 200 Examples in ARES/MARS and pd......Page 201 Inline sound processing......Page 203 Time-Domain Graphical Editing and Processing......Page 204 Analysis/Resynthesis Packages......Page 206 Structure of a Digital Signal Processor......Page 208 Memory Management......Page 210 Internal Arithmetics......Page 211 The Pipeline......Page 213 The ear......Page 215 Sound Intensity......Page 217 Psychophysics......Page 221 Pitch......Page 223 Masking......Page 225 Spatial sound perception......Page 227 References......Page 228