| Preface |
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xiii | |
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1 Complex Aperture Theory -- Volume Apertures -- General Results |
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1 | (40) |
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1.1 Coupling Transmitted and Received Electrical Signals to the Fluid Medium |
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1 | (5) |
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1.1.1 Transmit Coupling Equation |
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1 | (3) |
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1.1.2 Receive Coupling Equation |
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4 | (2) |
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1.2 The Near-Field Beam Pattern of a Volume Aperture |
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6 | (22) |
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6 | (15) |
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21 | (7) |
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1.3 The Far-Field Beam Pattern of a Volume Aperture |
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28 | (13) |
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28 | (5) |
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33 | (2) |
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35 | (1) |
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36 | (3) |
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Appendix 1B Important Functions and their Units at a Transmit and Receive Volume Aperture |
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39 | (2) |
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2 Complex Aperture Theory -- Linear Apertures |
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41 | (62) |
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2.1 The Far-Field Beam Pattern of a Linear Aperture |
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41 | (3) |
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2.2 Amplitude Windows and Corresponding Far-Field Beam Patterns |
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44 | (19) |
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2.2.1 The Rectangular Amplitude Window |
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45 | (3) |
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2.2.2 The Triangular Amplitude Window |
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48 | (4) |
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2.2.3 The Cosine Amplitude Window |
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52 | (5) |
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2.2.4 The Hanning, Hamming, and Blackman Amplitude Windows |
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57 | (6) |
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63 | (7) |
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70 | (3) |
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2.5 Beamwidth at an Arbitrary Beam-Steer Angle |
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73 | (8) |
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2.6 The Near-Field Beam Pattern of a Linear Aperture |
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81 | (22) |
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84 | (1) |
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2.6.2 Beam Steering and Aperture Focusing |
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85 | (1) |
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86 | (4) |
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Appendix 2A Transmitter and Receiver Sensitivity Functions of a Continuous Line Transducer |
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90 | (2) |
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Appendix 2B Radiation from a Linear Aperture |
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92 | (6) |
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Appendix 2C Symmetry Properties and Far-Field Beam Patterns |
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98 | (2) |
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Appendix 2D Computing the Normalization Factor |
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100 | (2) |
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Appendix 2E Summary of One-Dimensional Spatial Fourier Transforms |
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102 | (1) |
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3 Complex Aperture Theory -- Planar Apertures |
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103 | (38) |
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3.1 The Far-Field Beam Pattern of a Planar Aperture |
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103 | (3) |
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3.2 The Far-Field Beam Pattern of a Rectangular Piston |
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106 | (5) |
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3.3 The Far-Field Beam Pattern of a Circular Piston |
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111 | (9) |
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120 | (2) |
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3.5 The Near-Field Beam Pattern of a Planar Aperture |
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122 | (19) |
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3.5.1 Beam Steering and Aperture Focusing |
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125 | (1) |
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126 | (3) |
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Appendix 3A Transmitter and Receiver Sensitivity Functions of a Planar Transducer |
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129 | (3) |
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Appendix 3B Radiation from a Planar Aperture |
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132 | (6) |
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Appendix 3C Computing the Normalization Factor |
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138 | (3) |
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4 Time-Average Radiated Acoustic Power |
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141 | (16) |
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4.1 Directivity and Directivity Index |
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141 | (7) |
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4.2 The Source Level of a Directional Sound-Source |
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148 | (9) |
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154 | (3) |
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157 | (34) |
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157 | (6) |
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5.2 Cross-Track (Slant-Range) Resolution |
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163 | (2) |
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5.3 Along-Track (Azimuthal) Resolution |
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165 | (4) |
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5.4 Slant-Range Ambiguity |
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169 | (3) |
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172 | (3) |
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5.6 A Rectangular-Piston Model for a Side-Looking Sonar |
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175 | (1) |
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5.7 Design and Analysis of a Side-Looking Sonar Mission |
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176 | (15) |
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176 | (7) |
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183 | (5) |
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188 | (3) |
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6 Array Theory -- Linear Arrays |
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191 | (86) |
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6.1 The Far-Field Beam Pattern of a Linear Array |
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191 | (24) |
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6.1.1 Even Number of Elements |
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192 | (15) |
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6.1.2 Odd Number of Elements |
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207 | (8) |
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6.2 Common Amplitude Weights and Corresponding Far-Field Beam Patterns |
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215 | (7) |
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6.3 Dolph-Chebyshev Amplitude Weights |
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222 | (9) |
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6.4 The Phased Array -- Beam Steering |
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231 | (4) |
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6.5 Far-Field Beam Patterns and the Spatial Discrete Fourier Transform |
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235 | (12) |
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239 | (8) |
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6.6 The Near-Field Beam Pattern of a Linear Array |
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247 | (30) |
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6.6.1 Beam Steering and Array Focusing |
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250 | (7) |
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257 | (4) |
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Appendix 6A Normalization Factor for the Array Factor for N Even and Odd |
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261 | (3) |
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Appendix 6B Transmitter and Receiver Sensitivity Functions of an Omnidirectional Point-Element |
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264 | (2) |
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Appendix 6C Radiation from an Omnidirectional Point-Source |
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266 | (5) |
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Appendix 6D One-Dimensional Spatial FIR Filters |
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271 | (2) |
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Appendix 6E Far-Field Beam Patterns and the Spatial Discrete Fourier Transform for N Even |
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273 | (4) |
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277 | (42) |
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7.1 General Definition of Array Gain for a Linear Array |
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277 | (4) |
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7.2 Acoustic Field Radiated by a Target |
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281 | (6) |
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7.3 Total Output Signal from a Linear Array due to the Target |
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287 | (17) |
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7.3.1 FFT Beamforming for Linear Arrays |
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298 | (6) |
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7.4 Total Output Signal from a Linear Array due to Ambient Noise and Receiver Noise |
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304 | (3) |
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7.5 Evaluation of the Equation for Array Gain |
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307 | (12) |
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312 | (1) |
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Appendix 7A Attenuation Coefficient of Seawater |
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313 | (2) |
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Appendix 7B Fourier Transform, Fourier Series Coefficients, Time-Average Power, and Power Spectrum via the DFT |
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315 | (4) |
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8 Array Theory -- Planar Arrays |
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319 | (62) |
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8.1 The Far-Field Beam Pattern of a Planar Array |
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319 | (28) |
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8.2 The Phased Array -- Beam Steering |
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347 | (10) |
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8.3 Far-Field Beam Patterns and the Two-Dimensional Spatial Discrete Fourier Transform |
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357 | (5) |
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8.4 The Near-Field Beam Pattern of a Planar Array |
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362 | (4) |
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8.4.1 Beam Steering and Array Focusing |
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364 | (2) |
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8.5 FFT Beamforming for Planar Arrays |
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366 | (15) |
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375 | (3) |
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Appendix 8A Two-Dimensional Spatial FIR Filters |
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378 | (1) |
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Appendix 8B Normalization Factor for the Array Factor |
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379 | (2) |
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9 Array Theory -- Volume Arrays |
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381 | (28) |
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9.1 The Far-Field Beam Pattern of a Cylindrical Array |
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381 | (19) |
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9.1.1 The Phased Array -- Beam Steering |
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387 | (13) |
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9.2 The Far-Field Beam Pattern of a Spherical Array |
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400 | (9) |
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9.2.1 The Phased Array -- Beam Steering |
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404 | (1) |
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405 | (4) |
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409 | (78) |
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409 | (12) |
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10.2 Computing the Scattering Function of an Object |
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421 | (3) |
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424 | (2) |
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426 | (16) |
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426 | (11) |
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437 | (5) |
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442 | (6) |
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442 | (4) |
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446 | (2) |
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10.6 A Statistical Model of the Scattering Function |
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448 | (8) |
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456 | (31) |
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456 | (14) |
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470 | (5) |
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475 | (1) |
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Appendix 10A Radiation from a Time-Harmonic, Omnidirectional Point-Source |
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476 | (7) |
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Appendix 10B Gradient of the Time-Independent, Free-Space, Green's Function |
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483 | (2) |
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485 | (2) |
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11 Real Bandpass Signals and Complex Envelopes |
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487 | (28) |
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11.1 Definitions and Basic Relationships |
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487 | (10) |
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11.1.1 Signal Energy and Time-Average Power |
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492 | (3) |
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11.1.2 The Power Spectrum |
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495 | (2) |
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11.1.3 Orthogonality Relationships |
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497 | (1) |
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11.2 The Complex Envelope of an Amplitude-and-Angle-Modulated Carrier |
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497 | (9) |
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11.2.1 The Bandpass Sampling Theorem |
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503 | (1) |
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11.2.2 Orthogonality Relationships |
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504 | (2) |
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11.3 The Quadrature Demodulator |
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506 | (9) |
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511 | (4) |
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12 Target Detection in the Presence of Reverberation and Noise |
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515 | (66) |
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12.1 A Binary Hypothesis-Testing Problem |
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515 | (5) |
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12.2 The Signal-to-Interference Ratio |
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520 | (7) |
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12.3 Probability of False Alarm and Decision Threshold |
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527 | (11) |
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12.4 Probability of Detection and Receiver Operating Characteristic Curves |
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538 | (43) |
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553 | (1) |
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Appendix 12A Mathematical Models of the Target Return and Reverberation Return |
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554 | (11) |
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Appendix 12B Derivation of the Denominator of the Signal-to-Interference Ratio |
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565 | (10) |
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Appendix 12C Table 12C-1 Marcum Q-Function Q(a,b) |
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575 | (2) |
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Appendix 12D How to Compute Values for σ0/σ1 |
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577 | (1) |
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578 | (3) |
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13 The Auto-Ambiguity Function and Signal Design |
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581 | (34) |
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13.1 The Rectangular-Envelope CW Pulse |
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581 | (16) |
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13.2 The Rectangular-Envelope LFM Pulse |
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597 | (18) |
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612 | (3) |
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14 Underwater Acoustic Communication Signals |
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615 | (52) |
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14.1 M-ary Frequency-Shift Keying |
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615 | (16) |
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14.1.1 Time-Domain Description |
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615 | (2) |
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14.1.2 Frequency Spectrum and Bandwidth |
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617 | (2) |
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14.1.3 Signal Energy and Time-Average Power |
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619 | (3) |
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14.1.4 Orthogonality Conditions |
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622 | (1) |
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623 | (8) |
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14.2 M-ary Quadrature Amplitude Modulation |
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631 | (19) |
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14.2.1 Time-Domain Description |
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631 | (8) |
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14.2.2 Frequency Spectrum and Bandwidth |
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639 | (2) |
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14.2.3 Signal Energy and Time-Average Power |
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641 | (7) |
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648 | (2) |
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14.3 Orthogonal Frequency-Division Multiplexing |
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650 | (17) |
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14.3.1 Time-Domain Description |
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650 | (1) |
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14.3.2 Frequency Spectrum and Bandwidth |
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651 | (4) |
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14.3.3 Signal Energy and Time-Average Power |
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655 | (3) |
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658 | (6) |
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664 | (3) |
| Bibliography |
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667 | (4) |
| Index |
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671 | |