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Foreword
John Chowning |
xiii |
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Preface |
xv |
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Acknowledgments |
xvi |
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1 |
Digital Signals and Sampling |
1 |
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1.1 |
Measuring the Ephemeral |
1 |
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1.2 |
Analog-to-Digital Conversion |
9 |
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1.3 |
Aliasing |
11 |
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1.4 |
Digital-to-Analog Conversion |
20 |
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1.5 |
Binary Numbers |
22 |
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1.6 |
Synchronization |
28 |
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1.7 |
Discretization |
28 |
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1.8 |
Precision and Accuracy |
29 |
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1.9 |
Quantization |
29 |
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1.10 |
Noise and Distortion |
33 |
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1.11 |
Information Density of Digital Audio |
38 |
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1.12 |
Codecs |
40 |
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1.13 |
Further Refinements |
42 |
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1.14 |
Cultural Impact of Digital Audio |
46 |
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Summary |
47 |
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2 |
Musical Signals |
49 |
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2.1 |
Why Imaginary Numbers? |
49 |
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2.2 |
Operating with Imaginary Numbers |
51 |
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2.3 |
Complex Numbers |
52 |
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2.4 |
de Moivre's Theorem |
62 |
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2.5 |
Euler's Formula |
64 |
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2.6 |
Phasors |
68 |
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2.7 |
Graphing Comlpex Signals |
86 |
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2.8 |
Spectra of Complex Sampled Signals |
87 |
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2.9 |
Multiplying Phasors |
89 |
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2.10 |
Graphing Complex Spectra |
92 |
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2.11 |
Analytic Signals |
95 |
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Summary |
100 |
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3 |
Spectral Analysis and Synthesis |
103 |
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3.1 |
Introduction to the Fourier Transform |
103 |
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3.2 |
Discrete Fourier Transform |
103 |
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3.3 |
Discrete Fourier Transform in Action |
125 |
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3.4 |
Inverse Discrete Fourier Transform |
134 |
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3.5 |
Analyzing Real-World Signals |
138 |
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3.6 |
Windowing |
141 |
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3.7 |
Fast Fourier Transform |
145 |
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3.8 |
Properties of the Discrete Fourier Transform |
147 |
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3.9 |
A Practical Hilbert Transform |
154 |
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Summary |
156 |
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4 |
Convolution |
159 |
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4.1 |
Rolling Shutter Camera |
159 |
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4.2 |
Defining Convolution |
161 |
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4.3 |
Numerical Examples of Convolution |
163 |
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4.4 |
Convolving Spectra |
168 |
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4.5 |
Convolving Sigals |
172 |
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4.6 |
Convolution and the Fourier Transform |
180 |
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4.7 |
Domain Symmetry between Signals and Spectra |
180 |
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4.8 |
Convolution and Sampling Theory |
187 |
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4.9 |
Convolution and Windowing |
187 |
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4.10 |
Correlation Functions |
191 |
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Summary |
193 |
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Suggested Reading |
194 |
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5 |
Filtering |
195 |
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5.1 |
Tape Recorder as a Model of Filtering |
195 |
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5.2 |
Introduction to Filtering |
199 |
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5.3 |
A Sample Filter |
201 |
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5.4 |
Finding the Frequency Response |
203 |
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5.5 |
Linearity and Time Invariance of Filters |
217 |
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5.6 |
FIR Filters |
218 |
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5.7 |
IIR Filters |
218 |
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5.8 |
Canonical Filter |
219 |
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5.9 |
Time Domain Behavior of Filters |
219 |
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5.10 |
Filtering as Convolution |
222 |
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5.11 |
Z Transform |
224 |
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5.12 |
Z Transform of the General Difference Equation |
232 |
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5.13 |
Filter Families |
244 |
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Summary |
261 |
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6 |
Resonance |
263 |
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6.1 |
The Derivative |
263 |
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6.2 |
Differential Equations |
276 |
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6.3 |
Mathematics of Resonance |
280 |
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Summary |
297 |
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7 |
The Wave Equation |
299 |
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7.1 |
One-Dimensional Wave Equation and String Motion |
299 |
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7.2 |
An Example |
307 |
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7.3 |
Modeling Vibration with Finite Difference Equations |
310 |
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7.4 |
Striking Points, Plucking Points, and Spectra |
319 |
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Summary |
324 |
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8 |
Acoustical Systems |
325 |
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8.1 |
Dissipation and Radiation |
325 |
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8.2 |
Acoustical Current |
326 |
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8.3 |
Linearity of Frictional Force |
329 |
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8.4 |
Inertance, Inductive Reactance |
332 |
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8.5 |
Compliance, Capacitive Reactance |
333 |
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8.6 |
Reactance and Alternating Current |
334 |
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8.7 |
Capacitive Reactance and Frequency |
335 |
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8.8 |
Inductive Reactance and Frequency |
336 |
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8.9 |
Combining Resistance, Reactance, and Alternating Current |
336 |
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8.10 |
Resistance and Alternating Current |
337 |
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8.11 |
Capacitance and Alternating Current |
337 |
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8.12 |
Acoustical Impedance |
339 |
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8.13 |
Sound Propagation and Sound Transmission |
344 |
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8.14 |
Input Impedance: Fingerprinting a Resonant System |
351 |
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8.15 |
Scattering Junctions |
357 |
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Summary |
360 |
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Suggested Reading |
362 |
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9 |
Sound Synthesis |
363 |
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9.1 |
Forms of Synthesis |
363 |
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9.2 |
A Graphical Patch Language for Synthesis |
365 |
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9.3 |
Amplitude Modulation |
384 |
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9.4 |
Frequency Modulation |
389 |
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9.5 |
Vocal Synthesis |
409 |
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9.6 |
Synthesizing Concert Hall Acoustics |
425 |
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9.7 |
Physical Modeling |
433 |
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9.8 |
Source Models and Receiver Models |
449 |
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Summary |
450 |
|
10 |
Dynamic Spectra |
453 |
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10.1 |
Gabor's Elementary Signal |
454 |
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10.2 |
The Short-Time Fourier Transform |
459 |
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10.3 |
Phase Vocoder |
486 |
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10.4 |
Improving on the Fourier Transform |
496 |
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10.5 |
Psychoacoustic Audio Encoding |
502 |
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Summary |
507 |
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Suggested Reading |
509 |
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Epilogue |
511 |
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Appendix |
513 |
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A.1 |
About Algebra |
513 |
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A.2 |
About Trigonometry |
514 |
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A.3 |
Series and Summations |
517 |
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A.4 |
Trigonometric Identities |
518 |
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A.5 |
Modulo Arithmetic and Congruence |
522 |
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A.6 |
Finite Difference Approximations |
523 |
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A.7 |
Walsh-Hadamard Transform |
525 |
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A.8 |
Sampling, Reconstruction, and Sinc Function |
526 |
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A.9 |
Fourier Shift Theorem |
528 |
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A.10 |
Spectral Effects of Ring Modulation |
529 |
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A.11 |
Derivation of the Reflection Coefficient |
530 |
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Notes |
533 |
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Glossary |
539 |
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References |
543 |
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Equation Index |
547 |
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