Fundamentals of acoustic field theory and space-time signal processing

Cover......Page 1
Half Title......Page 2
Title Page......Page 4
Copyright Page......Page 5
Dedication......Page 6
Table of Contents......Page 8
Part I:  Acoustic Field Theory......Page 16
 Chapter 1: The Linear Wave Equation and Fundamental Acoustical Quantities......Page 18
  1.1 Equations of Motion......Page 19
  1.2 Equation of Continuity......Page 34
  1.3 Equation of State and The Speed of Sound......Page 36
  1.4 Derivation of the Linear Wave Equation......Page 40
  1.5 Time-Average Intensity Vector and Time-Average Power......Page 52
  1.6 Sound-Pressure Level, Source Level, Transmission Loss, and Sound-Intensity Level......Page 55
  Problems......Page 56
  Appendix 1A......Page 57
  Appendix 1B......Page 59
  Bibliography......Page 61
  2.1 Solution of the Linear Three-Dimensional Homogeneous Wave Equation......Page 62
   2.2.1 Time-Harmonic Solution of the Homogeneous Wave Equation......Page 68
   2.2.2 Group Speeds, Phase Speeds, and Wavelengths......Page 74
   2.2.3 Solution of the Homogeneous Wave Equation for Arbitrary Time Dependence......Page 80
  2.3 Reflection and Transmission Coefficients......Page 84
  2.4 The Rectangular Cavity......Page 118
  2.5 Waveguide with Rectangular Cross-Sectional Area......Page 127
   2.6.1 Solution of the Homogeneous Helmholtz Equation......Page 136
   2.6.2 Solution of the Inhomogeneous Helmholtz Equation......Page 139
   2.7.1 Free-Space Solution......Page 141
   2.7.2 Solution in the Presence of Boundaries......Page 150
  2.8 Integral Representations of the Time-Independent Free-Space Green's Function in Rectangular Coordinates......Page 153
  Problems......Page 156
  Appendix 2A......Page 160
  Appendix 2B......Page 162
  Appendix 2C......Page 163
  Bibliography......Page 165
  3.1 Solution of the Linear Three-Dimensional Homogeneous Wave Equation......Page 166
   3.2.1 Radiation from a Vibrating Cylinder......Page 176
   3.2.2 Monopole and Dipole Modes of Vibration......Page 179
  3.3 The Cylindrical Cavity......Page 188
  3.4 Waveguide with Circular Cross-Sectional Area......Page 194
  3.5 Scattering by a Cylinder......Page 199
  3.6 Integral Representations of the Time-Independent Free-Space Green’s Function in Cylindrical Coordinates......Page 207
  3.7 Reflection and Transmission of Spherical Waves at Planar Boundaries......Page 212
   3.8.1 Pressure-Release Surface with a Rigid Bottom......Page 219
   3.8.2 Pressure-Release Surface with a Fluid Bottom......Page 237
  3.9 Waveguide Model of the Ocean: Full-Wave Solution......Page 255
  Problems......Page 271
  Appendix 3A......Page 273
  Appendix 3B......Page 275
  Appendix 3C......Page 280
  Bibliography......Page 283
  4.1 Solution of the Linear Three-Dimensional Homogeneous Wave Equation......Page 284
   4.2.1 Radiation from a Vibrating Sphere......Page 295
   4.2.2 Monopole and Dipole Modes of Vibration......Page 297
  4.3 The Spherical Cavity......Page 307
  4.4 Scattering by a Sphere......Page 311
  Problems......Page 320
  Bibliography......Page 321
  5.1 The WKB Approximation......Page 322
   5.2.1 Transport and Eikonal Equations......Page 340
   5.2.2 Solution of the Eikonal Equation......Page 345
   5.2.3 Ray Equations......Page 352
   5.2.4 Amplitude Calculations Along Rays—Solution of the Transport Equation......Page 374
   5.2.5 Acoustic Pressure Calculations for Depth-Dependent Speeds of Sound Valid at Turning Points and Focal Points......Page 382
  5.3 The Parabolic Equation Approximation......Page 393
  Problems......Page 404
  Appendix 5A......Page 406
  Appendix 5B......Page 408
  Bibliography......Page 412
Part II: Space-Time Signal Processing......Page 414
  6.1 Coupling Transmitted and Received Electrical Signals to the Fluid Medium......Page 416
   6.2.1 Near-Field Directivity Functions......Page 420
   6.2.2 Far-Field Directivity Functions......Page 430
   6.3.1 Amplitude Windows......Page 435
   6.3.2 Beamwidth......Page 459
   6.3.3 Beam Steering......Page 466
   6.4.1 Aperture Focusing......Page 476
   6.4.2 Beam Steering and Aperture Focusing......Page 479
  6.5 Planar Apertures and Far-Field Directivity Functions......Page 480
   6.5.1 Beam Steering......Page 482
   6.5.2 Separable Functions—Rectangular Coordinates......Page 484
   6.5.3 Separable Functions—Polar Coordinates......Page 487
   6.6.1 Beam Steering and Aperture Focusing......Page 495
  6.7 Directivity Index......Page 498
  Problems......Page 503
  Appendix 6A......Page 508
  Bibliography......Page 510
   7.1.1 Product Theorem......Page 512
   7.1.2 Amplitude Weighting......Page 522
   7.1.3 The Phased Array (Beam Steering)......Page 533
   7.1.4 Far-Field Beam Patterns and The Discrete Fourier Transform......Page 535
  7.2 Linear Arrays and Near-Fie!d Directivity Functions......Page 547
   7.2.1 Beam Steering and Array Focusing......Page 548
  7.3 Array Gain......Page 550
   7.4.1 Product Theorem......Page 562
   7.4.2 Concentric Circular Arrays......Page 572
   7.4.3 The Phased Array (Beam Steering)......Page 574
  7.5 Planar Arrays and Near-Field Directivity Functions......Page 576
   7.5.1 Beam Steering and Array Focusing......Page 578
   7.6.1 Cylindrical Arrays......Page 579
   7.6.2 Spherical Arrays......Page 584
  Problems......Page 587
  Bibliography......Page 594
  8.1 FFT Beamforming for Planar Arrays......Page 596
  8.2 Complex Envelopes......Page 614
   8.3.1 Derivation and Interpretation......Page 630
   8.3.2 The Normalized Auto-Ambiguity Functions of Rectangular-Envelope CW and LFM Pulses......Page 640
  8.4 Time Compression /Stretch Factor, Time Delay, and Doppler Shift Expressions......Page 653
  Problems......Page 658
  Appendix 8A......Page 660
  Bibliography......Page 664
  9.1 Impulse Response and Transfer Function......Page 666
  9.2 Bifrequency Function......Page 673
  9.3 Output Frequency and Angular Spectrum......Page 675
  9.4 Coupling Equations and Pulse Propagation......Page 677
  Bibliography......Page 692
Symbols and Abbreviations......Page 694
Index......Page 700