Applications in Time-Frequency Signal Processing (Electrical Engineering & Applied Signal Processing Series)

✍ Scribed by Antonia Papandreou-Suppappola

• Publisher: CRC Press
• Year: 2002
• Tongue: English
• Leaves: 407
• Edition: 1
• Category: Library

✦ Synopsis

Because most real-world signals, including speech, sonar, communication, and biological signals, are non-stationary, traditional signal analysis tools such as Fourier transforms are of limited use because they do not provide easily accessible information about the localization of a given frequency component. A more suitable approach for those studying non-stationary signals is the use of time frequency representations that are functions of both time and frequency.Applications in Time-Frequency Signal Processing investigates the use of various time-frequency representations, such as the Wigner distribution and the spectrogram, in diverse application areas. Other books tend to focus on theoretical development. This book differs by highlighting particular applications of time-frequency representations and demonstrating how to use them. It also provides pseudo-code of the computational algorithms for these representations so that you can apply them to your own specific problems.Written by leaders in the field, this book offers the opportunity to learn from experts. Time-Frequency Representation (TFR) algorithms are simplified, enabling you to understand the complex theories behind TFRs and easily implement them. The numerous examples and figures, review of concepts, and extensive references allow for easy learning and application of the various time-frequency representations.

✦ Table of Contents

000fb74c_medium......Page 1
0065fm.pdf......Page 2
APPLICATIONS IN TIME-FREQUENCY SIGNAL PROCESSING......Page 5
Dedication......Page 7
Preface......Page 8
Acknowledgments......Page 12
Editor......Page 13
Contributors......Page 14
Contents......Page 16
1.1 Introduction......Page 17
Table of Contents......Page 0
1.1.1 Demand for time–frequency processing techniques......Page 18
1.1.2.1 Challenges in wireless communications......Page 19
1.1.2.2.1 Graphic demonstration......Page 20
1.1.2.2.2 Implementation issues. The WD can be implemented using the......Page 22
1.1.3 Importance of theoretical concepts......Page 23
1.2.1 Time-varying signal models......Page 24
1.2.3.1 Instantaneous frequency and group delay transforms......Page 26
1.2.3.2 Matched signal transforms......Page 28
1.2.4 Time–frequency representations of two output variables......Page 29
1.2.4.2 Quadratic TFRs......Page 30
1.2.5 Time–frequency representation implementation......Page 31
1.3.1 Multitude of quadratic time–frequency representations......Page 32
1.3.2 Quadratic time–frequency classification based on properties......Page 33
1.3.3.1 Theoretical formulation......Page 36
1.3.3.2 Cohen’s class QTFR examples......Page 37
1.3.3.3 Implementation algorithms......Page 39
1.3.4.1 Theoretical formulation......Page 40
1.3.4.2 Affine class QTFR examples......Page 41
1.3.4.3 Implementation algorithms......Page 43
1.3.5.1 Theoretical formulation......Page 44
1.3.5.2.1 Hyperbolic class......Page 45
1.3.5.2.2 Power classes......Page 47
1.4.1 Constant and linear time–frequency structures......Page 49
1.4.2 Constant and hyperbolic time–frequency structures......Page 50
1.4.3 Constant and exponential time–frequency structures......Page 51
1.4.4 Constant and power time–frequency structures......Page 52
1.4.5 Power time–frequency structures with real data......Page 55
1.5.1.1 Time-varying channel characterization......Page 56
1.5.1.4 Time-varying jamming interference mitigation......Page 57
1.5.4 Detection, estimation and classification......Page 58
1.6 Concluding Remarks......Page 60
Acknowledgments......Page 61
References......Page 62
Appendix A: Acronyms in Alphabetical Order......Page 98
Appendix B: Mathematical Notation in Alphabetical Order......Page 100
2.1 Overview......Page 101
2.2 Global Positioning System Signal Structure......Page 104
2.3 Interference Mitigation in Direct Sequence Spread-spectrum Systems......Page 105
2.4.1 Periodic signals in the time–frequency domain......Page 107
2.4.2 Symbol-period jammers......Page 109
2.4.3 General periodic jammers......Page 112
2.4.4 Discussions on cross-correlation coefficients......Page 116
2.4.5 In the presence of several satellite signals......Page 124
2.4.6 Subspace array processing......Page 127
References......Page 134
3.1 Introduction......Page 137
3.2 Positive Distributions: Brief History, Formulation and Relation to Bilinear Distributions......Page 139
3.2.1 Relation between the positive distribution formulation and the bilinear formulation......Page 141
3.2.3 Significance of bilinearity......Page 143
3.2.4 The cross-term issue......Page 145
3.2.5 Random signals......Page 146
3.3 Joint Densities and Conditional Densities......Page 148
3.3.1 Conditional means, standard deviations, and proper or realizable quantities......Page 149
3.3.2 Positive distributions, first conditional moments and instantaneous frequency: an example......Page 150
3.4.1 Is P(t,omega) a time-varying spectrum?......Page 151
3.4.2 Strong finite support......Page 154
3.5 Uncertainty Principle, Positive Distributions and Wigner Distribution......Page 155
3.5.1 Local variances: is there an uncertainty principle?......Page 156
3.6.1 Maximum entropy......Page 160
3.6.2 Least squares......Page 161
3.6.3 Deconvolution......Page 162
3.7 Collection of Examples and Plausibility of Results......Page 163
References......Page 171
4.1 Introduction......Page 179
4.2 Time–Frequency Distributions......Page 180
4.2.1 Types of time–frequency distributions......Page 181
4.3.1 Example 1: elastic cylindrical shell......Page 182
4.3.2 Example 2: underwater vehicle......Page 186
4.4 Feature Extraction and Classification from Time–Frequency Distributions......Page 189
4.4.1 Sonar signal classification......Page 190
References......Page 191
5.1 Introduction......Page 194
5.2.1 Motivation example......Page 195
5.2.2 Reassignment basics......Page 197
5.2.2.2 Localization vs. interference......Page 198
5.2.2.3 Reassignment principle......Page 199
5.2.3.1 Linear chirps......Page 200
5.2.3.2 Nonlinear FM signals......Page 203
5.2.3.3 Localization vs. resolution......Page 204
5.3.1.2 More reliable algorithm......Page 205
5.3.1.2.2......Page 207
5.3.1.3 Computing window derivative......Page 208
5.3.2.1 Reassigned smoothed pseudo-Wigner–Ville distributions......Page 210
5.3.2.2 Reassigned scalograms......Page 212
5.4 Real Case Studies......Page 214
References......Page 216
6.1 Introduction......Page 219
6.1.1 Time–frequency filters......Page 220
6.1.3 Style and organization of this chapter......Page 221
6.2.1.2 Zadeh filter......Page 222
6.2.2 On-line implementation of Zadeh filter......Page 223
6.3.1 Weyl symbol......Page 224
6.3.1.1 Halfband filters......Page 225
6.3.2 Weyl filter......Page 226
6.3.2.2 Input halfband Weyl filter......Page 227
6.3.3 Halfband Weyl filter......Page 229
6.3.3.1 Definition and calculation of halfband Weyl filter......Page 230
6.3.3.2 Implementation of the halfband Weyl filter......Page 231
6.3.3.3 Approximate halfband Weyl filter......Page 232
6.3.4.1 On-line implementation of minimum-energy Weyl filter......Page 233
6.3.4.3 On-line implementation of approximate halfband Weyl filter......Page 235
6.4.1 Time-varying bandpass filter......Page 238
6.4.2 Separation and denoising of chirp signals......Page 239
6.4.3 Generation of nonstationary random processes......Page 242
6.4.4 FM demodulation......Page 243
6.5.1.1 STFT......Page 245
6.5.1.2 STFT filter......Page 246
6.5.1.4 Underspread property of the STFT filter......Page 247
6.5.2 Choice of Windows......Page 248
6.5.2.1 Equal analysis and synthesis windows......Page 249
6.5.3 On-line implementation of short-time Fourier transform filter......Page 250
6.5.4 Multiwindow short-time Fourier transform filter......Page 252
6.5.5 Choice of prototype system......Page 254
6.5.5.1 First design method......Page 255
6.5.5.2 Second design method......Page 256
6.6.1.1 Gabor transform......Page 258
6.6.1.3 Comparison of Gabor filter with Zadeh filter......Page 259
6.6.1.4 Gabor filter and underspread property......Page 260
6.6.2.1 Choice of TF lattice parameters......Page 261
6.6.2.2 Choice of windows......Page 262
6.6.3 On-line implementation of Gabor filter......Page 263
6.6.4 Multiwindow Gabor filter......Page 266
6.6.4.2 On-line implementation of multiwindow Gabor filter......Page 267
6.6.5.1 Choice of TF lattice parameters......Page 268
6.6.5.3 Design example......Page 269
6.7.1 Time-varying bandpass filter......Page 270
6.7.2 Separation and denoising of frequency-modulated signals......Page 271
6.7.3 Adaptive speech enhancement......Page 273
6.8 Conclusions......Page 276
References......Page 279
7.1 Introduction......Page 286
7.2 Reduced Interference Distributions......Page 287
7.2.2 Reduced interference distribution kernels......Page 288
7.3 Discrete Time–Frequency Distributions......Page 290
7.3.1 Generalized discrete time–frequency distributions......Page 291
7.3.1.2 Analytical signal......Page 296
7.3.2 Fast algorithms for discrete reduced interference distributions......Page 297
7.3.2.1 Windowing......Page 298
7.3.3 Comparisons of group delay, time–frequency distributions......Page 299
7.4 Applications......Page 302
7.4.1 Underwater acoustics......Page 303
7.4.4 Temporomandibular joint sounds......Page 304
7.4.5 Heart sounds and muscle sounds......Page 306
7.4.7.1 High energy plasma discharges......Page 308
7.4.7.2 Turbulent air flow......Page 309
References......Page 313
gdtfdo.m......Page 317
quasi-Wigner.m......Page 318
Copyright Notice......Page 319
8.1 Introduction......Page 320
8.2 Seismic Sequence Analysis......Page 322
8.3 Time–Frequency Representations for Seismic Signal Analysis......Page 325
8.4 Seismic Attribute Extraction......Page 330
8.5 Hybrid linear and Quadratic Time–Frequency Seismic Attributes......Page 335
8.6 Three-dimensional Seismic Attribute Extraction......Page 339
8.7 Conclusions......Page 348
References......Page 349
9.1 Introduction......Page 351
9.1.2 Nonstationary and multicomponent characteristics of the electroencephalogram......Page 352
9.1.3 Electroencephalographic acquisition......Page 353
9.2.1 Basic definitions and relationships......Page 354
9.2.2 Time–frequency distribution selection......Page 357
9.2.3.1 Seizure criteria for the autocorrelation method......Page 358
9.2.3.2 Mapping of autocorrelation seizure criteria to time–frequency domain......Page 359
9.2.4 From frequency domain to time–frequency domain......Page 360
9.2.5 Time–frequency patterns......Page 363
9.3.1.1 Class A (linear frequency-modulated patterns with a quasi-constant frequency)......Page 365
9.3.1.2 Class B (short linear frequency-modulated patterns with a Quasi-constant frequency)......Page 366
9.3.2 Piecewise linear frequency-modulated patterns......Page 368
9.4.2 Class F (activities lacking a specific pattern)......Page 369
9.5 Time–Frequency Matched Detector......Page 371
9.5.1.2 Signal restructuring......Page 372
9.5.1.5 Amplitude and length criteria......Page 374
9.5.2 Experimental setup......Page 375
9.5.2.1 Electroencephalogram model......Page 376
9.5.2.3 Threshold selection......Page 377
9.6 Discussion and Conclusions......Page 378
References......Page 379
10.1 Introduction......Page 382
10.2 Background and Definitions......Page 383
10.2.1 Example illustrations......Page 384
10.3 Class-Dependent Time–Frequency Representations......Page 387
10.3.1 Class-dependent kernel method......Page 388
10.3.2 Traditional kernel design......Page 389
10.3.3 Kernel design with euclidean distances......Page 390
10.4 Illustrative Example: Underwater Transient Identification......Page 391
10.4.1 Linear predictive coefficient method......Page 392
10.4.2 Class-dependent kernel method......Page 393
10.5 Kernel Design with Fisher’s Discriminant Metric......Page 394
10.6 Application to Speech Recognition......Page 396
10.6.2 Mel-frequency cepstral coefficients and hidden markov model phone recognition system......Page 397
10.6.3 Time–frequency isolated phone recognition......Page 399
10.6.4 Hybrid system phone recognition......Page 400
10.7 English Alphabet Recognition......Page 401
10.7.1 Experimental results......Page 402
10.8 Conclusions......Page 404
References......Page 405