Foreword |
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v | |
Preface |
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vii | |
Acknowledgments |
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xi | |
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1 | (72) |
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3 | (18) |
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1.1 Functions and Signals |
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3 | (5) |
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4 | (2) |
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1.1.2 Functions of Frequency |
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6 | (2) |
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1.2 Fundamental Concepts of Spectrum |
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8 | (6) |
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1.2.1 Periodicity and Pitch |
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8 | (2) |
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1.2.2 Distributed Spectra |
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10 | (1) |
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11 | (1) |
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1.2.4 The Uncertainty Principle |
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12 | (2) |
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1.3 Psychoacoustic Aspects |
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14 | (4) |
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1.3.1 The Cochlear Mechanism |
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15 | (1) |
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16 | (1) |
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1.3.3 Loudness Perception |
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17 | (1) |
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1.4 A Provisional Definition |
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18 | (3) |
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2 A History of the Spectrum |
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21 | (29) |
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2.1 Principles of Pitch and Scale |
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21 | (4) |
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2.1.1 The Pythagorean Scale |
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22 | (1) |
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23 | (1) |
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2.1.3 Musical Instruments |
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24 | (1) |
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25 | (5) |
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2.2.1 Frequency and Pitch |
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25 | (1) |
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26 | (1) |
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2.2.3 Strings and the Wave Equation |
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26 | (2) |
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28 | (1) |
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28 | (2) |
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2.2.6 Partials and Hearing |
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30 | (1) |
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30 | (7) |
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2.3.1 Musical Tones and Noise |
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31 | (1) |
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2.3.2 Resonators and Other Analytical Instruments |
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32 | (2) |
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2.3.3 Theory of Spectral Hearing |
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34 | (1) |
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35 | (1) |
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2.3.5 Rayleigh's Theory of Sound |
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36 | (1) |
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37 | (13) |
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2.4.1 Electronic Instruments and Signal Processing |
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37 | (3) |
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40 | (1) |
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41 | (9) |
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3 Fundamental Aspects of Audio and Music Signals |
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50 | (23) |
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3.1 The Nature of Audio Signals |
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50 | (3) |
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51 | (1) |
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3.1.2 Instantaneous Frequency and Phase |
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52 | (1) |
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3.2 Manipulating Analogue Audio Signals |
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53 | (8) |
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3.2.1 Non-Linear Distortion |
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55 | (2) |
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3.2.2 Noise and Signal Level |
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57 | (1) |
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58 | (2) |
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60 | (1) |
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61 | (12) |
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63 | (3) |
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3.3.2 The Discrete-Time Baseband |
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66 | (4) |
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70 | (3) |
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73 | (310) |
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4 Continuous and Discrete Spectra |
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75 | (31) |
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75 | (4) |
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4.1.1 Even and Odd Functions |
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76 | (1) |
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4.1.2 Interpreting the Fourier Formula |
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76 | (2) |
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4.1.3 The Fourier Series of a Square Wave |
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78 | (1) |
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4.1.4 Complex Representation |
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78 | (1) |
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4.2 The Fourier Transform |
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79 | (6) |
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4.2.1 The Inverse Fourier Transform |
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80 | (1) |
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4.2.2 Amplitude and Phase Spectra |
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80 | (1) |
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4.2.3 The Spectra of Real Signals |
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80 | (3) |
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4.2.4 The Spectra of Fundamental Signals |
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83 | (2) |
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85 | (4) |
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4.3.1 Discrete Convolution |
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86 | (3) |
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4.4 Sampling in Time and Frequency |
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89 | (7) |
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4.4.1 Finite-Time Signals |
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91 | (3) |
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4.4.2 Hard-Sync Waveforms |
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94 | (2) |
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96 | (6) |
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98 | (1) |
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98 | (2) |
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100 | (1) |
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101 | (1) |
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102 | (4) |
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5 Discrete Time, Discrete Frequency |
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106 | (50) |
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5.1 The Discrete Fourier Transform |
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106 | (12) |
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5.1.1 Programming the DFT |
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107 | (3) |
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5.1.2 Interpreting the DFT |
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110 | (3) |
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113 | (5) |
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5.2 The Fast Fourier Transform |
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118 | (12) |
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118 | (4) |
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5.2.2 ReaTto-Complex and Complex-to-Real Transforms |
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122 | (5) |
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127 | (3) |
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5.3 Discrete-Time Convolution |
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130 | (18) |
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131 | (5) |
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136 | (3) |
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5.3.3 Partitioned Convolution |
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139 | (3) |
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5.3.4 Multiple Partitions |
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142 | (3) |
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5.3.5 Spectral Design Applications |
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145 | (3) |
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5.4 Time-Varying Convolution |
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148 | (4) |
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149 | (1) |
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5.4.2 Spectral Design Applications |
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149 | (3) |
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5.5 The Discrete Spectrum |
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152 | (4) |
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6 Time-Frequency Processing |
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156 | (48) |
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156 | (2) |
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6.1.1 Designing a Bandpass Filter |
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156 | (1) |
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157 | (1) |
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6.2 The Short-Time Fourier Transform |
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158 | (6) |
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6.2.1 Analysis Frame Rate |
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160 | (1) |
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161 | (1) |
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162 | (2) |
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6.3 Spectral Analysis-Synthesis |
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164 | (8) |
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6.3.1 Phase Difference Method |
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166 | (1) |
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6.3.2 Instantaneous Frequencies |
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167 | (2) |
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169 | (1) |
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170 | (1) |
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171 | (1) |
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6.4 Streaming Spectral Processing |
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172 | (10) |
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6.4.1 The Spectral Analysis--Synthesis Class |
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172 | (7) |
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6.4.2 Spectral Signals in Csound |
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179 | (3) |
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6.5 Spectral Manipulation |
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182 | (13) |
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182 | (1) |
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183 | (3) |
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186 | (1) |
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186 | (1) |
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6.5.5 Mixing and Demixing |
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187 | (1) |
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6.5.6 Frequency Scaling and Shifting |
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187 | (2) |
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189 | (4) |
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193 | (1) |
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193 | (2) |
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6.6 Timescale Modifications |
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195 | (3) |
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196 | (1) |
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6.6.2 Pitch and Timescale |
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197 | (1) |
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198 | (1) |
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6.7 The Hilbert Transform |
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198 | (2) |
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200 | (4) |
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204 | (65) |
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205 | (4) |
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205 | (1) |
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7.1.2 Inverse Comb Filter |
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206 | (3) |
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209 | (2) |
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7.2.1 Complex Polynomials |
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210 | (1) |
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210 | (1) |
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7.2.3 The Z-Transform and the DFT |
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211 | (1) |
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7.3 Zeros on the Complex Plane |
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211 | (7) |
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7.3.1 First-Order Filters |
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213 | (1) |
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7.3.2 Second-Order Filters |
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214 | (2) |
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216 | (1) |
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217 | (1) |
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218 | (6) |
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218 | (1) |
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7.4.2 Frequency-Domain Method |
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219 | (2) |
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221 | (3) |
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224 | (7) |
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225 | (1) |
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226 | (3) |
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229 | (1) |
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230 | (1) |
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7.6 Recursive Filter Design |
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231 | (22) |
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7.6.1 Parallel and Series Connections |
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231 | (5) |
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7.6.2 Modeling Physical Systems |
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236 | (1) |
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237 | (5) |
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242 | (6) |
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7.6.5 The Channel Vocoder |
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248 | (5) |
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253 | (9) |
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254 | (3) |
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7.7.2 Audio-Rate Coefficient Modulation |
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257 | (2) |
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7.7.3 Delay Time Modulation |
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259 | (3) |
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7.8 A Generalized Concept of Spectrum |
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262 | (7) |
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8 Non-Linear Synthesis of Spectra |
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269 | (51) |
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8.1 Closed-Form Synthesis Formulae |
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270 | (10) |
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8.1.1 Generalized Summation Methods |
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273 | (7) |
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8.2 Frequency and Phase Modulation Synthesis |
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280 | (12) |
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281 | (1) |
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8.2.2 Signal Bandwidth and Aliasing |
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282 | (2) |
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8.2.3 Carrier to Modulator Ratio |
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284 | (1) |
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285 | (1) |
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8.2.5 Frequency Modulation |
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286 | (1) |
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8.2.6 Splitting Sidebands |
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287 | (1) |
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288 | (1) |
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289 | (2) |
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291 | (1) |
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8.3 Phase Distortion Synthesis |
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292 | (4) |
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8.3.1 Vector Phase Shaping |
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293 | (3) |
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8.4 Modified Frequency Modulation Synthesis |
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296 | (5) |
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8.4.1 Phase-synchronous ModFM |
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296 | (3) |
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299 | (2) |
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8.5 Polynomial Waveshaping |
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301 | (10) |
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302 | (2) |
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304 | (1) |
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304 | (3) |
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8.5.4 Chebyshev Polynomials |
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307 | (2) |
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8.5.5 Quadrature Waveshaping |
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309 | (2) |
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8.6 Other Distortion Functions |
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311 | (2) |
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8.7 Adaptive Modulation Methods |
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313 | (2) |
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8.7.1 Adaptive Frequency Modulation |
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314 | (1) |
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8.8 The Non-Linear Spectrum |
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315 | (5) |
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320 | (63) |
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9.1 Random Processes and Noise Signals |
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321 | (7) |
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9.1.1 Centroid and Bandwidth |
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321 | (1) |
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9.1.2 Probability Distribution and Density |
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322 | (1) |
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9.1.3 Power Spectrum Density |
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323 | (2) |
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325 | (1) |
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325 | (3) |
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328 | (6) |
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9.2.1 Random Number Generators |
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329 | (2) |
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331 | (1) |
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332 | (1) |
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332 | (1) |
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333 | (1) |
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334 | (8) |
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9.3.1 Asynchronous Granular Synthesis |
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334 | (3) |
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337 | (4) |
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341 | (1) |
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9.4 The Spectral Envelope Revisited |
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342 | (12) |
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342 | (1) |
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9.4.2 Computing Prediction Coefficients |
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343 | (3) |
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346 | (1) |
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9.4.4 Spectral Representations |
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347 | (5) |
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9.4.5 Streaming Linear Prediction |
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352 | (2) |
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354 | (24) |
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355 | (2) |
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9.5.2 Peak Identification |
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357 | (1) |
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358 | (1) |
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359 | (4) |
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9.5.5 Frequency and Phase |
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363 | (2) |
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365 | (5) |
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9.5.7 Residual Extraction |
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370 | (3) |
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9.5.8 Modeling the Residual |
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373 | (2) |
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375 | (1) |
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9.5.10 Streaming Partial Track Processing |
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375 | (2) |
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377 | (1) |
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9.6 The Non-Deterministic Spectrum |
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378 | (5) |
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383 | (92) |
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10 Spectral Design in Music |
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385 | (29) |
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10.1 The Emergence of Spectral Color as a Structuring Device |
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386 | (5) |
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10.1.1 Chords and Spectra |
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387 | (1) |
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10.1.2 Instrumentation and Spectra |
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388 | (3) |
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391 | (3) |
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10.2.1 Recording and Broadcasting as Carriers of Spectral Information |
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391 | (1) |
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10.2.2 Changes in Instrumental Sound |
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392 | (1) |
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10.2.3 The Mechano-Acoustic and the Electro-Acoustic |
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393 | (1) |
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394 | (4) |
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10.3.1 The Feedback on Instrumental Writing |
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395 | (1) |
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10.3.2 Electric Jazz, Rock, and Pop |
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396 | (1) |
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397 | (1) |
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398 | (1) |
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398 | (12) |
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399 | (2) |
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401 | (9) |
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10.5 The Musical Spectrum |
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410 | (4) |
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414 | (35) |
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414 | (7) |
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418 | (3) |
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11.2 Non-Linear Distortion |
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421 | (8) |
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421 | (4) |
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11.2.2 Synthesis of Resonance |
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425 | (4) |
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11.3 Source-Modifier Techniques |
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429 | (6) |
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430 | (3) |
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433 | (2) |
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435 | (2) |
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437 | (8) |
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11.5.1 Spectral Envelopes |
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438 | (2) |
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440 | (1) |
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441 | (2) |
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443 | (2) |
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445 | (4) |
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12 Composing the Spectrum |
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449 | (26) |
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12.1 Spectral Music-Making |
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449 | (5) |
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450 | (1) |
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451 | (1) |
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12.1.3 Realtime Systems and Performance |
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451 | (1) |
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12.1.4 Physical and Virtual Space |
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452 | (1) |
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12.1.5 Approaches to Composing the Spectrum |
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453 | (1) |
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12.2 The Composition of Mouvements |
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454 | (19) |
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12.2.1 The Generative Principle |
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454 | (2) |
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456 | (6) |
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462 | (5) |
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467 | (4) |
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471 | (2) |
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12.3 Conclusion: the Spectral Playground |
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473 | (2) |
References |
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475 | (8) |
Index |
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483 | |