Introduction To Digital Signal Processing: Computer Musically Speaking

CONTENTS......Page 14
Preface......Page 6
Acknowledgements......Page 10
About the Book Cover Design......Page 12
1 Introduction......Page 22
2 The Sine Tone......Page 23
3.1 Duration......Page 25
3.2 Pitch......Page 26
3.3.1 Sound intensity level (SIL)......Page 27
3.3.4 Equal loudness curve......Page 29
3.4 Auditory masking......Page 32
4 Sampling: The Art of Being Discrete......Page 34
4.1 Sampling theorem......Page 39
4.2 Aliasing......Page 41
5 Quantization and Pulse Code Modulation (PCM)......Page 47
5.1 SNR and QSNR......Page 49
6 DC Component......Page 50
7 Distortion and SquareWaves......Page 52
7.1 Dithering......Page 54
8 Musical Examples......Page 58
References and Further Reading......Page 59
1 Introduction......Page 61
2 Amplitude Envelope and ADSR......Page 62
3 Wavetable Synthesis......Page 64
4.1 Windowing:More details......Page 67
4.2 RMS and amplitude envelope......Page 71
5 Time-Domain Fundamental Frequency Computation......Page 74
5.1 Zero-crossing rate......Page 75
5.2 Autocorrelation......Page 79
5.3 Cross-correlation......Page 85
6.1 Up-sampling......Page 86
6.2 Down-sampling......Page 87
7 Overlap and Add (OLA)......Page 89
7.1 OLA: Problems and solutions......Page 92
8 Musical Examples......Page 93
References and Further Reading......Page 95
2 Granular Synthesis......Page 96
2.1 Basic granular synthesis parameters......Page 97
2.2 Asynchronous granular synthesis......Page 100
2.3 Pitch shifting and time stretching/compression......Page 101
3 Amplitude Distortion and Waveshaping......Page 102
3.1 Dynamic compressor......Page 104
3.2 Distortion......Page 106
3.3 Dynamic expander......Page 107
3.5 Waveshaping synthesis......Page 108
3.5.1 Chebychev polynomials of the 1st kind......Page 109
4.1 Equal power panning......Page 112
4.2.1 Echo, chorus, and flanging......Page 113
5 Musical Examples......Page 116
References and Further Reading......Page 117
1 Introduction......Page 118
2 Sinusoids Revisited......Page 119
3 Imaginary, Complex Numbers, and Euler’s Formula......Page 120
3.1 Euler’s formula......Page 122
4.1 Beating......Page 123
4.2 Amplitude modulation and ring modulation......Page 126
4.3 Amplitude modulation (AM)......Page 127
4.4.1 Ring modulation with complex signals......Page 129
5 Sinusoidal Modulation Techniques II: Frequency......Page 131
5.1 FM: Sidebands and the Bessel function......Page 132
5.2 Modulation index......Page 136
5.3 General topics in FM control parameters......Page 137
6 Musical Examples......Page 139
References and Further Reading......Page 142
1 Introduction......Page 143
2 Difference Equations: Starting with the Moving Average Algorithm......Page 144
2.2 Difference equations: General form......Page 146
3 Linear-Time Invariant (LTI) Systems......Page 148
3.1 Linearity property: Scalability and superposition......Page 149
3.2 Time-invariance property: Time-shift invariance......Page 150
3.3 Importance of LTI systems in DSP......Page 152
4 Impulse Response......Page 153
4.1 Finite impulse response (FIR) and infinite impulse response (IIR)......Page 156
4.2 Stability and IIR systems......Page 157
5 Convolution......Page 159
5.1 Convolution “Need to Knows”......Page 161
6 System Diagrams and Digital Building Blocks......Page 162
7 Musical Examples......Page 164
1 Introduction......Page 166
2 The Frequency Response......Page 167
2.1.1 Frequency range and Nyquist revisited......Page 170
2.1.2 H(ejθ) and periodicity property......Page 175
2.1.3 Symmetry......Page 176
2.2 More stuff on the frequency response......Page 177
3 Phase Response and Phase Distortion......Page 181
3.1 Phase delay......Page 184
3.2 Linearity and phase......Page 186
3.3 Phase response and continuous phase......Page 188
3.4 Group delay......Page 189
4 The (Almost) Magical Z-Transform......Page 193
4.1 What does all this mean? Part I......Page 195
4.2 What does all this mean? Part II: poles and zeros......Page 196
4.3 What does all this mean? Part III: the unit circle and the z-plane......Page 197
5 Region of Convergence (ROC)......Page 202
5.1 Causal system ROC.......Page 207
5.2 Mixed-causality systems......Page 208
6 Stability and the Unit Circle......Page 209
7 The Inverse Z-Transform......Page 211
7.1 Long division method......Page 212
7.2 Taylor series expansion method......Page 214
7.3 Contour integration/residue theorem method......Page 216
8 Useful Tools in MATLABR......Page 218
9 Musical Examples......Page 219
References and Further Reading......Page 220
1 Introduction......Page 221
2 Low/High/Band-Pass and Band-Stop Filters......Page 222
2.1 Filter design specifications......Page 224
2.2 Passband, stopband, and transition band......Page 225
2.4 Filter order, filter sharpness, and ripple......Page 226
2.5 MATLABR  filter design tools......Page 240
3 Filter Examples......Page 243
3.1 Subtractive synthesis and filters......Page 244
3.2 Bi-quadratic filter (a.k.a. Bi-quad filter) and theWah-Wah filter......Page 246
3.3 The Comb-filter......Page 254
3.3.1 Comb-filter interpretation......Page 256
3.3.2 Comb-filter examples......Page 259
3.4 String vibration and standing waves......Page 263
3.5 Physical modeling synthesis and the plucked stringmodel......Page 266
3.5.1 Direct implementation of di.erence equations......Page 274
3.6.1 The chorus effect......Page 275
3.6.2 Multi-tap filters and filter banks......Page 277
3.6.3 Fractional delay......Page 280
3.6.4 The flanger effect......Page 282
3.6.5 The all-pass filter......Page 283
3.6.6 Very basic all-pass filter reverb......Page 287
4 Musical Examples......Page 293
References and Further Reading......Page 295
1 Introduction......Page 297
2 Additive Synthesis......Page 298
3 The Fourier Transform......Page 301
4 The Discrete-Time Fourier Transform (DTFT) and the Discrete Fourier Transform(DFT)......Page 302
4.1 Magnitude, Phase, and Other Basic Properties of the DFT......Page 309
4.2 Time Resolution vs. Frequency Resolution in DFTs......Page 310
5 Short-Time Fourier Transform (STFT)......Page 313
6 Zero Padding......Page 314
7 Aliasing Revisited......Page 316
8.1 Down-Sampling......Page 319
8.2 Up-Sampling......Page 323
9 Windowing Revisited: A View from the Frequency-Domain Side......Page 325
9.2 Hann Window......Page 331
9.3 Hamming Window......Page 332
9.5 Chebychev and Kaiser Windows......Page 333
9.6 Not Just More Windowing Stuff......Page 334
10 The Fast Fourier Transform (FFT)......Page 340
11 Convolution (also) Revisited......Page 342
11.1 Circular Convolution and Time-Aliasing......Page 343
12 OneMore Look at Dithering......Page 346
13 Spectrogram......Page 348
14 Fourier Transform Properties and Summary......Page 350
16 Musical Examples......Page 352
References and Further Reading......Page 353
1.1 Musical signals and important nomenclatures......Page 354
2 Spectral Analysis......Page 356
2.2 Log vs. linear......Page 357
2.3 Spectral peaks, valleys, and spectral envelope......Page 361
2.4 Extraction of fundamental frequency and harmonics......Page 365
2.4.1 Inverse comb-filtering......Page 366
2.4.2 Cepstrum analysis......Page 370
2.4.3 Harmonic product spectrum......Page 371
3.1 Channel-vocoder......Page 373
3.1.1 Filter banks, envelope followers, and the encoder......Page 375
3.1.2 Voiced and unvoiced analysis and the decoder......Page 377
3.1.3.1 Zero-crossing analysis......Page 380
3.1.3.3 Low-band to full-band energy ratio......Page 384
3.1.3.4 Spectral flatness measure......Page 385
3.2 Linear predictive coding (LPC)......Page 387
3.3 LPC coefficient computation......Page 392
3.4 The phase vocoder......Page 394
3.4.1 Estimation of instantaneous frequency......Page 396
3.4.2 Phase unwrapping......Page 398
3.4.3 Phase vocoder: Filter-bank interpretation......Page 400
3.4.4 Phase vocoder: Fourier transform interpretation......Page 406
3.4.5 Phase vocoder basics: Time and pitch-shifting......Page 411
3.4.5.1 Time-shifting......Page 412
3.4.5.2 Pitch-shifting......Page 417
4.1 Salient feature extraction......Page 418
4.1.1 Spectral envelope......Page 419
4.1.2 Spectral centroid......Page 420
4.1.4 Spectral flux......Page 421
4.1.6 Roll-off......Page 422
4.1.8 Amplitude modulation (Tremolo)......Page 423
4.2 MIR (Music information retrieval)......Page 424
4.2.1 Query-by-humming (QbH)......Page 425
4.2.2 Automatic beat detection and rhythm analysis......Page 426
4.2.3 Automatic timbre recognition......Page 427
4.3 FMS (feature modulation synthesis)......Page 428
5 Musical Examples......Page 430
References and Further Reading......Page 432
1.1 Equal temperament scale......Page 436
1.3 Bark scale......Page 437
1.4 Mel scale......Page 438
2 MATLAB Programs Used in This Book......Page 439
References and Further Reading......Page 443
Index......Page 444