Discrete-time speech signal processing: principles and practice

Contents......Page 8
Foreword......Page 16
Preface......Page 18
 1.1 Discrete-Time Speech Signal Processing......Page 22
 1.2 The Speech Communication Pathway......Page 23
 1.3 Analysis/Synthesis Based on Speech Production and Perception......Page 24
 1.4 Applications......Page 26
 1.5 Outline of Book......Page 28
 Bibliography......Page 30
 2.2 Discrete-Time Signals......Page 32
 2.3 Discrete-Time Systems......Page 35
 2.4 Discrete-Time Fourier Transform......Page 36
 2.5 Uncertainty Principle......Page 41
 2.6 z-Transform......Page 44
 2.7 LTI Systems in the Frequency Domain......Page 49
  2.8.1 Difference Equation Realization......Page 54
  2.8.2 Magnitude-Phase Relationships......Page 55
  2.8.4 IIR Filters......Page 58
 2.9 Time-Varying Systems......Page 59
 2.10 Discrete Fourier Transform......Page 62
  2.11.1 Sampling Theorem......Page 64
  2.11.2 Sampling a System Response......Page 66
 2.12 Summary......Page 68
 Exercises......Page 69
 Bibliography......Page 75
 3.1 Introduction......Page 76
  3.2.1 Lungs......Page 78
  3.2.2 Larynx......Page 79
  3.2.3 Vocal Tract......Page 87
  3.2.4 Categorization of Sound by Source......Page 92
 3.3 Spectrographic Analysis of Speech......Page 93
 3.4 Categorization of Speech Sounds......Page 98
  3.4.1 Elements of a Language......Page 100
  3.4.2 Vowels......Page 102
  3.4.3 Nasals......Page 105
  3.4.4 Fricatives......Page 106
  3.4.5 Plosives......Page 109
  3.4.6 Transitional Speech Sounds......Page 113
 3.5 Prosody: The Melody of Speech......Page 116
  3.6.1 Acoustic Cues......Page 120
  3.6.2 Models of Speech Perception......Page 121
 3.7 Summary......Page 122
 Exercises......Page 123
 Bibliography......Page 129
 4.1 Introduction......Page 132
  4.2.1 Basics......Page 133
  4.2.2 The Wave Equation......Page 136
  4.3.1 Lossless Case......Page 140
  4.3.2 Effect of Energy Loss......Page 148
  4.3.3 Boundary Effects......Page 151
  4.3.4 A Complete Model......Page 155
 4.4 A Discrete-Time Model Based on Tube Concatenation......Page 157
  4.4.1 Sound Propagation in the Concatenated Tube Model......Page 158
  4.4.2 A Discrete-Time Realization......Page 164
  4.4.3 Complete Discrete-Time Model......Page 169
 4.5 Vocal Fold/Vocal Tract Interaction......Page 174
  4.5.1 A Model for Source/Tract Interaction......Page 175
  4.5.2 Formant Frequency and Bandwidth Modulation......Page 179
 Exercises......Page 183
 Bibliography......Page 194
 5.1 Introduction......Page 196
 5.2 Time-Dependent Processing......Page 197
  5.3.1 Formulation......Page 198
  5.3.2 Error Minimization......Page 202
  5.3.3 Autocorrelation Method......Page 206
  5.3.4 The Levinson Recursion and Its Associated Properties......Page 215
  5.3.5 Lattice Filter Formulation of the Inverse Filter......Page 221
  5.3.6 Frequency-Domain Interpretation......Page 226
  5.4.1 Formulation......Page 228
  5.4.2 Error Minimization......Page 230
  5.5.1 Time Domain......Page 231
  5.5.2 Frequency Domain......Page 233
 5.6 Synthesis Based on All-Pole Modeling......Page 237
 5.7 Pole-Zero Estimation......Page 241
  5.7.1 Linearization......Page 242
  5.7.2 Application to Speech......Page 243
  5.7.3 High-Pitched Speakers: Using Two Analysis Windows......Page 248
  5.8.1 Model......Page 249
  5.8.2 Estimation......Page 251
 5.9 Summary......Page 253
  Random Processes......Page 254
  Ensemble Averages......Page 256
  Time Averages......Page 257
  Power Density Spectrum......Page 258
 Appendix 5.B: Derivation of the Lattice Filter in Linear Prediction Analysis......Page 259
 Exercises......Page 261
 Bibliography......Page 272
 6.1 Introduction......Page 274
 6.2 Concept......Page 275
 6.3 Homomorphic Systems for Convolution......Page 278
  6.4.1 Sequences with Rational z-Transforms......Page 282
  6.4.2 Impulse Trains Convolved with Rational z-Transform Sequences......Page 286
  6.4.3 Homomorphic Filtering......Page 287
  6.4.4 Discrete Complex Cepstrum......Page 290
 6.5 Spectral Root Homomorphic Filtering......Page 293
 6.6 Short-Time Homomorphic Analysis of Periodic Sequences......Page 297
  6.6.1 Quefrency-Domain Perspective......Page 298
  6.6.2 Frequency-Domain Perspective......Page 300
  6.7.1 Complex Cepstrum of Voiced Speech......Page 302
  6.7.2 Complex Cepstrum of Unvoiced Speech......Page 307
 6.8 Analysis/Synthesis Structures......Page 308
  6.8.1 Zero- and Minimum-Phase Synthesis......Page 309
  6.8.2 Mixed-Phase Synthesis......Page 311
  6.8.3 Spectral Root Deconvolution......Page 313
  6.9.2 Homomorphic Prediction......Page 314
 6.10 Summary......Page 317
 Exercises......Page 318
 Bibliography......Page 327
 7.1 Introduction......Page 330
  7.2.1 Fourier Transform View......Page 331
  7.2.2 Filtering View......Page 334
  7.2.3 Time-Frequency Resolution Tradeoffs......Page 339
  7.3.1 Formulation......Page 341
  7.3.2 Filter Bank Summation (FBS) Method......Page 342
  7.3.3 Overlap-Add (OLA) Method......Page 346
  7.3.4 Time-Frequency Sampling......Page 349
 7.4 Short-Time Fourier Transform Magnitude......Page 351
  7.4.1 Signal Representation......Page 352
  7.4.2 Reconstruction from Time-Frequency Samples......Page 355
 7.5 Signal Estimation from the Modified STFT or STFTM......Page 356
  7.5.1 Heuristic Application of STFT Synthesis Methods......Page 358
  7.5.2 Least-Squared-Error Signal Estimation from the Modified STFT......Page 361
  7.5.3 LSE Signal Estimation from Modified STFTM......Page 363
  7.6.1 Time-Scale Modification......Page 364
  7.6.2 Noise Reduction......Page 370
 7.7 Summary......Page 371
 Appendix 7.A: FBS Method with Multiplicative Modification......Page 372
 Exercises......Page 373
 Bibliography......Page 382
 8.1 Introduction......Page 384
 8.2 Revisiting the FBS Method......Page 385
  8.3.1 Analysis/Synthesis of Quasi-Periodic Signals......Page 388
  8.3.2 Applications......Page 396
  8.3.3 Motivation for a Sinewave Analysis/Synthesis......Page 401
  8.4.1 Preservation of Temporal Envelope......Page 402
  8.4.2 Phase Coherence of Quasi-Periodic Signals......Page 406
 8.5 Constant-Q Analysis/Synthesis......Page 407
  8.5.1 Motivation......Page 408
  8.5.2 Wavelet Transform......Page 409
  8.5.3 Discrete Wavelet Transform......Page 413
  8.5.4 Applications......Page 418
 8.6 Auditory Modeling......Page 422
  8.6.1 AM-FM Model of Auditory Processing......Page 424
  8.6.2 Auditory Spectral Model......Page 427
  8.6.3 Phasic/Tonic View of Auditory Neural Processing......Page 429
 Exercises......Page 433
 Bibliography......Page 443
 9.1 Introduction......Page 448
 9.2 Sinusoidal Speech Model......Page 450
 9.3 Estimation of Sinewave Parameters......Page 453
  9.3.1 Voiced Speech......Page 456
  9.3.2 Unvoiced Speech......Page 460
  9.3.3 Analysis System......Page 461
  9.3.4 Frame-to-Frame Peak Matching......Page 463
 9.4 Synthesis......Page 466
  9.4.1 Cubic Phase Interpolation......Page 467
  9.4.2 Overlap-Add Interpolation......Page 471
  9.4.3 Examples......Page 473
  9.4.4 Applications......Page 477
  9.4.5 Time-Frequency Resolution......Page 478
  9.5.1 Signal Model......Page 481
  9.5.2 Applications......Page 482
  9.6.1 Signal Model......Page 495
  9.6.2 Analysis/Synthesis......Page 496
  9.6.3 Application to Signal Modification......Page 498
 9.7 Summary......Page 499
 Appendix 9.A: Derivation of the Sinewave Model......Page 500
 Appendix 9.B: Derivation of Optimal Cubic Phase Parameters......Page 503
 Exercises......Page 505
 Bibliography......Page 520
 10.1 Introduction......Page 524
 10.2 A Correlation-Based Pitch Estimator......Page 525
 10.3 Pitch Estimation Based on a "Comb Filter"......Page 526
 10.4 Pitch Estimation Based on a Harmonic Sinewave Model......Page 530
  10.4.1 Parameter Estimation for the Harmonic Sinewave Model......Page 531
  10.4.2 Parameter Estimation for the Harmonic Sinewave Model with a priori Amplitude......Page 532
  10.4.3 Voicing Detection......Page 537
  10.4.4 Time-Frequency Resolution Perspective......Page 540
  10.4.5 Evaluation by Harmonic Sinewave Reconstruction......Page 543
  10.5.1 A Phase Model Based on Onset Time......Page 544
  10.5.2 Onset Estimation......Page 546
  10.5.3 Sinewave Amplitude Envelope Estimation......Page 548
  10.5.4 Minimum-Phase Sinewave Reconstruction......Page 551
  10.6.1 Harmonic Sinewave Model......Page 552
  10.6.2 Multi-Band Voicing......Page 554
 10.7 Summary......Page 555
 Exercises......Page 556
 Bibliography......Page 561
 11.1 Introduction......Page 562
 11.2 The STFT and Wavelet Transform Revisited......Page 563
  11.2.2 Minimum Uncertainty......Page 564
  11.2.3 Tracking Instantaneous Frequency......Page 567
  11.3.1 Properties of a Proper Time-Frequency Distribution......Page 570
  11.3.2 Spectrogram as a Time-Frequency Distribution......Page 573
  11.3.3 Wigner Distribution......Page 574
  11.3.5 Application to Speech Analysis......Page 579
 11.4 Aeroacoustic Flow in the Vocal Tract......Page 583
  11.4.1 Preliminaries......Page 584
  11.4.2 Early Measurements and Hypotheses of Aeroacoustic Flow in the Vocal Tract......Page 585
  11.4.3 Aeroacoustic Mechanical Model......Page 588
  11.4.4 Aeroacoustic Computational Model......Page 591
  11.5.1 Motivation......Page 592
  11.5.2 Energy Measurement......Page 593
  11.5.3 Energy Separation......Page 598
 11.6 Summary......Page 603
 Exercises......Page 604
 Bibliography......Page 613
 12.1 Introduction......Page 616
 12.3 Scalar Quantization......Page 619
  12.3.1 Fundamentals......Page 620
  12.3.2 Quantization Noise......Page 623
  12.3.3 Derivation of the Max Quantizer......Page 627
  12.3.4 Companding......Page 630
  12.3.5 Adaptive Quantization......Page 631
  12.3.6 Differential and Residual Quantization......Page 634
  12.4.1 Approach......Page 637
  12.4.2 VQ Distortion Measure......Page 639
  12.4.3 Use of VQ in Speech Transmission......Page 641
  12.5.1 Subband Coding......Page 642
  12.5.2 Sinusoidal Coding......Page 646
  12.6.1 Basic Linear Prediction Coder (LPC)......Page 656
  12.6.2 A VQ LPC Coder......Page 658
  12.6.3 Mixed Excitation LPC (MELP)......Page 659
 12.7 LPC Residual Coding......Page 661
  12.7.1 Multi-Pulse Linear Prediction......Page 662
  12.7.2 Multi-Pulse Modeling with Long-Term Prediction......Page 666
  12.7.3 Code-Excited Linear Prediction (CELP)......Page 670
 12.8 Summary......Page 673
 Exercises......Page 674
 Bibliography......Page 681
 13.1 Introduction......Page 686
  13.2.1 Problem Formulation......Page 687
  13.2.2 Spectral Subtraction......Page 689
  13.2.3 Cepstral Mean Subtraction......Page 692
 13.3 Wiener Filtering......Page 693
  13.3.1 Basic Approaches to Estimating the Object Spectrum......Page 694
  13.3.2 Adaptive Smoothing Based on Spectral Change......Page 696
  13.3.3 Application to Speech......Page 699
  13.3.4 Optimal Spectral Magnitude Estimation......Page 701
 13.4 Model-Based Processing......Page 703
 13.5 Enhancement Based on Auditory Masking......Page 705
  13.5.1 Frequency-Domain Masking Principles......Page 706
  13.5.2 Calculation of the Masking Threshold......Page 708
  13.5.3 Exploiting Frequency Masking in Noise Reduction......Page 709
  13.6.1 Formulation......Page 711
  13.6.2 Temporal Filtering......Page 712
  13.6.3 Nonlinear Transformations of Time-Trajectories......Page 715
 13.7 Summary......Page 719
 Appendix 13.A: Stochastic-Theoretic Parameter Estimation......Page 720
 Exercises......Page 721
 Bibliography......Page 726
 14.1 Introduction......Page 730
  14.2.1 Formulation......Page 732
  14.2.2 Mel-Cepstrum......Page 733
  14.2.3 Sub-Cepstrum......Page 736
  14.3.1 Minimum-Distance Classifier......Page 738
  14.3.2 Vector Quantization......Page 739
  14.3.3 Gaussian Mixture Model (GMM)......Page 740
  14.4.1 Glottal Flow Derivative......Page 746
  14.4.3 Relative Influence of Source, Spectrum, and Prosody......Page 750
 14.5 Signal Enhancement for the Mismatched Condition......Page 754
  14.5.1 Linear Channel Distortion......Page 755
  14.5.2 Nonlinear Channel Distortion......Page 758
  14.5.3 Other Approaches......Page 767
  14.6.1 Synthesized Coded Speech......Page 769
  14.6.2 Experiments with Coder Parameters......Page 770
 14.7 Summary......Page 772
 Appendix 14.A: Expectation-Maximization (EM) Estimation......Page 773
 Exercises......Page 775
 Bibliography......Page 783
 Speech Signal Processing......Page 788
 Databases......Page 789
 A......Page 790
 D......Page 791
 G......Page 792
 L......Page 793
 O......Page 794
 P......Page 795
 S......Page 796
 T......Page 798
 V......Page 799
 Z......Page 800
About the Author......Page 802