 اسم المؤلف
Kihong Shin
التاريخ
27 أكتوبر 2018
المشاهدات
167
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Fundamentals of Signal Processing for Sound and Vibration Engineers
Kihong Shin
Andong National University
Republic of Korea
Joseph K. Hammond
University of Southampton
Contents
Preface ix
1 Introduction to Signal Processing 1
1.1 Descriptions of Physical Data (Signals) 6
1.2 Classification of Data 7
Part I Deterministic Signals 17
2 Classification of Deterministic Data 19
2.1 Periodic Signals 19
2.2 Almost Periodic Signals 21
2.3 Transient Signals 24
2.4 Brief Summary and Concluding Remarks 24
2.5 MATLAB Examples 26
3 Fourier Series 31
3.1 Periodic Signals and Fourier Series 31
3.2 The Delta Function 38
3.3 Fourier Series and the Delta Function 41
3.4 The Complex Form of the Fourier Series 42
3.5 Spectra 43
3.6 Some Computational Considerations 46
3.7 Brief Summary 52
3.8 MATLAB Examples 52
4 Fourier Integrals (Fourier Transform) and Continuous-Time Linear Systems 57
4.1 The Fourier Integral 57
4.2 Energy Spectra 61
4.3 Some Examples of Fourier Transforms 62
4.4 Properties of Fourier Transforms 67vi CONTENTS
4.5 The Importance of Phase 71
4.6 Echoes 72
4.7 Continuous-Time Linear Time-Invariant Systems and Convolution 73
4.8 Group Delay (Dispersion) 82
4.9 Minimum and Non-Minimum Phase Systems 85
4.10 The Hilbert Transform 90
4.11 The Effect of Data Truncation (Windowing) 94
4.12 Brief Summary 102
4.13 MATLAB Examples 103
5 Time Sampling and Aliasing 119
5.1 The Fourier Transform of an Ideal Sampled Signal 119
5.2 Aliasing and Anti-Aliasing Filters 126
5.3 Analogue-to-Digital Conversion and Dynamic Range 131
5.4 Some Other Considerations in Signal Acquisition 134
5.5 Shannon’s Sampling Theorem (Signal Reconstruction) 137
5.6 Brief Summary 139
5.7 MATLAB Examples 140
6 The Discrete Fourier Transform 145
6.1 Sequences and Linear Filters 145
6.2 Frequency Domain Representation of Discrete Systems and Signals 150
6.3 The Discrete Fourier Transform 153
6.4 Properties of the DFT 160
6.5 Convolution of Periodic Sequences 162
6.6 The Fast Fourier Transform 164
6.7 Brief Summary 166
6.8 MATLAB Examples 170
Part II Introduction to Random Processes 191
7 Random Processes 193
7.1 Basic Probability Theory 193
7.2 Random Variables and Probability Distributions 198
7.3 Expectations of Functions of a Random Variable 202
7.4 Brief Summary 211
7.5 MATLAB Examples 212
8 Stochastic Processes; Correlation Functions and Spectra 219
8.1 Probability Distribution Associated with a Stochastic Process 220
8.2 Moments of a Stochastic Process 222
8.3 Stationarity 224
8.4 The Second Moments of a Stochastic Process; Covariance
(Correlation) Functions 225
8.5 Ergodicity and Time Averages 229
8.6 Examples 232CONTENTS vii
8.7 Spectra 242
8.8 Brief Summary 251
8.9 MATLAB Examples 253
9 Linear System Response to Random Inputs: System Identification 277
9.1 Single-Input Single-Output Systems 277
9.2 The Ordinary Coherence Function 284
9.3 System Identification 287
9.4 Brief Summary 297
9.5 MATLAB Examples 298
10 Estimation Methods and Statistical Considerations 317
10.1 Estimator Errors and Accuracy 317
10.2 Mean Value and Mean Square Value 320
10.3 Correlation and Covariance Functions 323
10.4 Power Spectral Density Function 327
10.5 Cross-spectral Density Function 347
10.6 Coherence Function 349
10.7 Frequency Response Function 350
10.8 Brief Summary 352
10.9 MATLAB Examples 354
11 Multiple-Input/Response Systems 363
11.1 Description of Multiple-Input, Multiple-Output (MIMO) Systems 363
11.2 Residual Random Variables, Partial and Multiple Coherence Functions 364
11.3 Principal Component Analysis 370
Appendix A Proof of  ? ??2M sin 2 2??aMaM da = 1 375
Appendix B Proof of |Sxy( f )|2 ? Sxx( f )Syy( f ) 379
Appendix C Wave Number Spectra and an Application 381
Appendix D Some Comments on the Ordinary Coherence
Function ?xy 2 ( f ) 385
Appendix E Least Squares Optimization: Complex-Valued Problem 387
Appendix F Proof of HW( f ) ? H1( f ) as ?( f ) ? ? 389
Appendix G Justification of the Joint Gaussianity of X( f ) 391
Appendix H Some Comments on Digital Filtering 393
References 395
Index 399
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