Table Of ContentSignals and Communication Technology
E. S. Gopi
Digital Speech
Processing Using
Matlab
Signals and Communication Technology
For furthervolumes:
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E. S. Gopi
Digital Speech Processing
Using Matlab
123
E.S. Gopi
Electronics andCommunication
Engineering
National InstituteofTechnology
Trichy, TamilNadu
India
ISSN 1860-4862 ISSN 1860-4870 (electronic)
ISBN 978-81-322-1676-6 ISBN 978-81-322-1677-3 (eBook)
DOI 10.1007/978-81-322-1677-3
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Dedicated to my wife G. Viji, my son
A. G. Vasig and my daughter A. G. Desna
Preface
The most of the applications of digital speech processing deal with speech or
speaker pattern recognition. To understand the practical implementation of the
speech or speaker recognition techniques, there is the need to understand the
concepts of digital speech processing and the pattern recognition. This book aims
ingivingthebalancedtreatmentofboththeconcepts.Thisbookdealswithspeech
processing concepts like speech production model, speech feature extraction,
speech compression, etc., and the basic pattern recognition concepts applied to
speech signals likePCA,LDA, ICA, SVM,HMM,GMM, BPN,KSOM, etc.The
book is written such that it is suitable for the beginners who are doing basic
research in digital speech processing. All the topics covered in this book are
illustrated using Matlab in almost all the topics for better understanding.
vii
Acknowledgments
I would like to thank Profs. S. Soundararajan (Director, NITT, Trichy),
M.Chidambaram(IITM,Chennai),K.M.M.Prabhu(IITM,Chennai),P.Palanisamy,
P. Somaskandan, B. Venkataramani, and S. Raghavan (NITT, Trichy) for their
support. I would also like to thank those who helped directly or indirectly in
bringing out this book successfully. Special thanks to my parents Mr. E. Sankara
Subbu and Mrs. E. S. Meena.
Thanks
E. S. Gopi
ix
Contents
1 Pattern Recognition for Speech Detection. . . . . . . . . . . . . . . . . . . 1
1.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Back-propagation Neural Network. . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Back-propagation Algorithm . . . . . . . . . . . . . . . . . . . 5
1.2.2 ANN Illustration . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Support Vector Machine. . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.1 Dual Problem to Solve (1.25)–(1.28) . . . . . . . . . . . . . 14
1.3.2 ‘‘Kernel-Trick’’ for Nonlinear Separation in SVM . . . . 15
1.3.3 Illustration for Support Vector Machine . . . . . . . . . . . 16
1.4 Hidden Markov Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.4.1 Baum–Welch Technique to Obtain the Unknown
Parameters in HMM. . . . . . . . . . . . . . . . . . . . . . . . . 26
1.4.2 Steps to Compute the Unknown Parameters of HMM
Using Expectation–Maximization Algorithm. . . . . . . . 28
1.4.3 Viterbi Algorithm to Compute the Generating
Probability of the Arbitrary Speech Segment. . . . . . . . 29
1.4.4 Isolated Word Recognition Using HMM. . . . . . . . . . . 30
1.4.5 Alignment Method to Model HMM . . . . . . . . . . . . . . 31
1.4.6 Illustration of Hidden Markov Model. . . . . . . . . . . . . 31
1.5 Gaussian Mixture Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
1.5.1 Steps Involved to Model GMM Using
Expectation–Maximization Algorithm. . . . . . . . . . . . . 39
1.5.2 Isolated Word Recognition Using GMM. . . . . . . . . . . 39
1.5.3 Illustration of GMM. . . . . . . . . . . . . . . . . . . . . . . . . 40
1.6 Unsupervised Learning System . . . . . . . . . . . . . . . . . . . . . . . 43
1.6.1 Need for Unsupervised Learning System . . . . . . . . . . 43
1.6.2 k-Means Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 43
1.6.3 Illustration of k-Means Algorithm . . . . . . . . . . . . . . . 44
1.6.4 Fuzzy k-Means Algorithm. . . . . . . . . . . . . . . . . . . . . 44
1.6.5 Steps Involved in Fuzzy k-Means Clustering. . . . . . . . 46
1.6.6 Illustration of Fuzzy k-Means Algorithm . . . . . . . . . . 46
1.6.7 Kohonen Self-Organizing Map . . . . . . . . . . . . . . . . . 48
1.6.8 Illustration of KSOM . . . . . . . . . . . . . . . . . . . . . . . . 51
xi
xii Contents
1.7 Dimensionality Reduction Techniques . . . . . . . . . . . . . . . . . . 53
1.7.1 Principal Component Analysis. . . . . . . . . . . . . . . . . . 53
1.7.2 Illustration of PCA Using 2D to 1D Conversion . . . . . 54
1.7.3 Illustration of PCA. . . . . . . . . . . . . . . . . . . . . . . . . . 54
1.7.4 Linear Discriminant Analysis . . . . . . . . . . . . . . . . . . 55
1.7.5 Small Sample Size Problem in LDA . . . . . . . . . . . . . 57
1.7.6 Null-Space LDA . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
1.7.7 Kernel LDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
1.7.8 Kernel-Trick to Execute LDA
in the Higher-Dimensional Space. . . . . . . . . . . . . . . . 59
1.7.9 Illustration of Dimensionality Reduction
Using LDA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
1.8 Independent Component Analysis . . . . . . . . . . . . . . . . . . . . . 64
1.8.1 Solving ICA Bases Using Kurtosis Measurement. . . . . 66
1.8.2 Steps to Obtain the ICA Bases . . . . . . . . . . . . . . . . . 68
1.8.3 Illustration of Dimensionality Reduction Using ICA. . . 68
2 Speech Production Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
2.2 1-D Sound Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
2.2.1 Physics on Sound Wave Travelling Through the Tube
with Uniform Cross-Sectional Area A. . . . . . . . . . . . . 74
2.2.2 Solution to (2.9) and (2.18). . . . . . . . . . . . . . . . . . . . 76
2.3 Vocal Tract Model as the Cascade Connections of Identical
Length Tubes with Different Cross-Sections . . . . . . . . . . . . . . 78
2.4 Modelling the Vocal Tract from the Speech Signal . . . . . . . . . 82
2.4.1 Autocorrelation Method . . . . . . . . . . . . . . . . . . . . . . 82
2.4.2 Auto Covariance Method . . . . . . . . . . . . . . . . . . . . . 87
2.5 Lattice Structure to Obtain Excitation Source
for the Typical Speech Signal . . . . . . . . . . . . . . . . . . . . . . . . 88
2.5.1 Computation of Lattice Co-efficient
from LPC Co-efficients . . . . . . . . . . . . . . . . . . . . . . 89
3 Feature Extraction of the Speech Signal. . . . . . . . . . . . . . . . . . . . 93
3.1 Endpoint Detection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.2 Dynamic Time Warping. . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.3 Linear Predictive Co-efficients . . . . . . . . . . . . . . . . . . . . . . . 100
3.4 Poles of the Vocal Tract. . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
3.5 Reflection Co-efficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.6 Log Area Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.7 Cepstrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.8 Line Spectral Frequencies. . . . . . . . . . . . . . . . . . . . . . . . . . . 108
3.9 Mel-Frequency Cepstral Co-efficients. . . . . . . . . . . . . . . . . . . 113
3.9.1 Gibbs Phenomenon . . . . . . . . . . . . . . . . . . . . . . . . . 117
3.9.2 Discrete Cosine Transformation. . . . . . . . . . . . . . . . . 118
Contents xiii
3.10 Spectrogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
3.10.1 Time Resolution Versus Frequency Resolution
in Spectrogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
3.11 Discrete Wavelet Transformation. . . . . . . . . . . . . . . . . . . . . . 124
3.12 Pitch Frequency Estimation. . . . . . . . . . . . . . . . . . . . . . . . . . 126
3.12.1 Autocorrelation Approach. . . . . . . . . . . . . . . . . . . . . 126
3.12.2 Homomorphic Filtering Approach . . . . . . . . . . . . . . . 127
3.13 Formant Frequency Estimation . . . . . . . . . . . . . . . . . . . . . . . 129
3.13.1 Formant Extraction Using Vocal Tract Model. . . . . . . 129
3.13.2 Formant Extraction Using Homomorphic Filtering. . . . 132
4 Speech Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
4.1 Uniform Quantization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
4.2 Nonuniform Quantization . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
4.3 Adaptive Quantization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
4.4 Differential Pulse Code Modulation. . . . . . . . . . . . . . . . . . . . 140
4.4.1 Illustrations of the Prediction of Speech
Signal Using lpc . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
4.5 Code-Excited Linear Prediction. . . . . . . . . . . . . . . . . . . . . . . 142
4.5.1 Estimation of the Delay Constant D. . . . . . . . . . . . . . 145
4.5.2 Estimation of the Gain Constants G1 and G2 . . . . . . . 146
4.6 Assessment of the Quality of the Compressed
Speech Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
Appendix A: Constrained Optimization Using
Lagrangian Techniques. . . . . . . . . . . . . . . . . . . . . . . . . 151
Appendix B: Expectation–Maximization Algorithm . . . . . . . . . . . . . . 157
Appendix C: Diagonalization of the Matrix . . . . . . . . . . . . . . . . . . . . 161
Appendix D: Condition Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Appendix E: Spectral Flatness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Appendix F: Functional Blocks of the Vocal Tract and the Ear . . . . . 175
About the Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
About the Book. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
