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| Foreword | |
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| Preface | |
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| Acknowledgments | |
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| Digital Signals and Sampling | |
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| Measuring the Ephemeral | |
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| Analog-to-Digital Conversion | |
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| Aliasing | |
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| Digital-to-Analog Conversion | |
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| Binary Numbers | |
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| Synchronization | |
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| Discretization | |
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| Precision and Accuracy | |
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| Quantization | |
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| Noise and Distortion | |
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| Information Density of Digital Audio | |
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| Codecs | |
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| Further Refinements | |
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| Cultural Impact of Digital Audio | |
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| Summary | |
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| Musical Signals | |
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| Why Imaginary Numbers? | |
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| Operating with Imaginary Numbers | |
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| Complex Numbers | |
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| de Moivre's Theorem | |
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| Euler's Formula | |
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| Phasors | |
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| Graphing Comlpex Signals | |
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| Spectra of Complex Sampled Signals | |
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| Multiplying Phasors | |
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| Graphing Complex Spectra | |
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| Analytic Signals | |
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| Summary | |
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| Spectral Analysis and Synthesis | |
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| Introduction to the Fourier Transform | |
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| Discrete Fourier Transform | |
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| Discrete Fourier Transform in Action | |
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| Inverse Discrete Fourier Transform | |
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| Analyzing Real-World Signals | |
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| Windowing | |
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| Fast Fourier Transform | |
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| Properties of the Discrete Fourier Transform | |
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| A Practical Hilbert Transform | |
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| Summary | |
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| Convolution | |
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| Rolling Shutter Camera | |
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| Defining Convolution | |
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| Numerical Examples of Convolution | |
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| Convolving Spectra | |
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| Convolving Sigals | |
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| Convolution and the Fourier Transform | |
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| Domain Symmetry between Signals and Spectra | |
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| Convolution and Sampling Theory | |
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| Convolution and Windowing | |
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| Correlation Functions | |
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| Summary | |
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| Suggested Reading | |
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| Filtering | |
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| Tape Recorder as a Model of Filtering | |
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| Introduction to Filtering | |
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| A Sample Filter | |
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| Finding the Frequency Response | |
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| Linearity and Time Invariance of Filters | |
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| FIR Filters | |
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| IIR Filters | |
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| Canonical Filter | |
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| Time Domain Behavior of Filters | |
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| Filtering as Convolution | |
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| Z Transform | |
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| Z Transform of the General Difference Equation | |
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| Filter Families | |
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| Summary | |
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| Resonance | |
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| The Derivative | |
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| Differential Equations | |
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| Mathematics of Resonance | |
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| Summary | |
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| The Wave Equation | |
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| One-Dimensional Wave Equation and String Motion | |
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| An Example | |
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| Modeling Vibration with Finite Difference Equations | |
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| Striking Points, Plucking Points, and Spectra | |
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| Summary | |
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| Acoustical Systems | |
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| Dissipation and Radiation | |
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| Acoustical Current | |
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| Linearity of Frictional Force | |
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| Inertance, Inductive Reactance | |
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| Compliance, Capacitive Reactance | |
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| Reactance and Alternating Current | |
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| Capacitive Reactance and Frequency | |
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| Inductive Reactance and Frequency | |
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| Combining Resistance, Reactance, and Alternating Current | |
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| Resistance and Alternating Current | |
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| Capacitance and Alternating Current | |
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| Acoustical Impedance | |
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| Sound Propagation and Sound Transmission | |
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| Input Impedance: Fingerprinting a Resonant System | |
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| Scattering Junctions | |
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| Summary | |
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| Suggested Reading | |
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| Sound Synthesis | |
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| Forms of Synthesis | |
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| A Graphical Patch Language for Synthesis | |
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| Amplitude Modulation | |
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| Frequency Modulation | |
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| Vocal Synthesis | |
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| Synthesizing Concert Hall Acoustics | |
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| Physical Modeling | |
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| Source Models and Receiver Models | |
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| Summary | |
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| Dynamic Spectra | |
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| Gabor's Elementary Signal | |
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| The Short-Time Fourier Transform | |
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| Phase Vocoder | |
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| Improving on the Fourier Transform | |
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| Psychoacoustic Audio Encoding | |
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| Summary | |
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| Suggested Reading | |
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| Epilogue | |
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| Appendix | |
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| About Algebra | |
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| About Trigonometry | |
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| Series and Summations | |
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| Trigonometric Identities | |
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| Modulo Arithmetic and Congruence | |
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| Finite Difference Approximations | |
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| Walsh-Hadamard Transform | |
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| Sampling, Reconstruction, and Sinc Function | |
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| Fourier Shift Theorem | |
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| Spectral Effects of Ring Modulation | |
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| Derivation of the Reflection Coefficient | |
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| Notes | |
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| Glossary | |
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| References | |
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| Equation Index | |