{"product_id":"underwater-acoustics-analysis-design-and-performance-of-sonar-hardback-9780470688755","title":"Underwater Acoustics; Analysis, Design and Performance of Sonar (Hardback) 9780470688755","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eUnderwater Acoustics\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eAnalysis, Design and Performance of Sonar\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eRichard P. Hodges (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780470688755, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 11 June 2010\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e384 pages\u003cbr\u003e25.2 x 17.3 x 2.5 cm, 0.794 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eOffering complete and comprehensive coverage of modern sonar spectrum system analysis, \u003ci\u003eUnderwater Acoustics: Analysis, Design and Performance of Sonar\u003c\/i\u003e provides a state-of-the-art introduction to the subject and has been carefully structured to offer a much-needed update to the classic text by Urick. Expanded to included computational approaches to the topic, this book treads the line between the highly theoretical and mathematical texts and the more populist, non-mathematical books that characterize the existing literature in the field. The author compares and contrasts different techniques for sonar design, analysis and performance prediction and includes key experimental and theoretical results, pointing the reader towards further detail with extensive references. Practitioners in the field of sonar design, analysis and performance prediction as well as graduate students and researchers will appreciate this new reference as an invaluable and timely contribution to the field.\u003cbr\u003e \u003cbr\u003e   \u003cp\u003eChapters include the sonar equation, radiated, self and ambient noise, active sonar sources, transmission loss, reverberation, transducers, active target strength, statistical detection theory, false alarms, contacts and targets, variability and uncertainty, modelling detections and tactical decision aids, cumulative probability of detection, tracking target motion analysis and localization, and design and evaluation of sonars\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eAbout the Author xiii\u003c\/p\u003e \u003cp\u003ePreface xv\u003c\/p\u003e \u003cp\u003eAcknowledgements xvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction to Sonar 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Acoustic Waves 1\u003c\/p\u003e \u003cp\u003e1.1.1 Compressions and Rarefactions 3\u003c\/p\u003e \u003cp\u003e1.2 Speed of Propagation 4\u003c\/p\u003e \u003cp\u003e1.3 Acoustic Wave Parameters 5\u003c\/p\u003e \u003cp\u003e1.4 Doppler Shift 9\u003c\/p\u003e \u003cp\u003e1.5 Intensity, SPL, and Decibels 10\u003c\/p\u003e \u003cp\u003e1.6 Combining Acoustic Waves 11\u003c\/p\u003e \u003cp\u003e1.7 Comparative Parameter for Sound in Water and Air 14\u003c\/p\u003e \u003cp\u003eReferences 15\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 The Sonar Equations 17\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Signal-to-Noise Ratio 17\u003c\/p\u003e \u003cp\u003e2.2 Active Sonar Equation 18\u003c\/p\u003e \u003cp\u003e2.3 Signal Excess 20\u003c\/p\u003e \u003cp\u003e2.4 Figure of Merit 20\u003c\/p\u003e \u003cp\u003eReferences 21\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Transducers, Directionality, and Arrays 23\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Transducer Response 25\u003c\/p\u003e \u003cp\u003e3.2 Beam Pattern Response 25\u003c\/p\u003e \u003cp\u003e3.3 Linear Arrays 27\u003c\/p\u003e \u003cp\u003e3.3.1 Triplet Towed Array 33\u003c\/p\u003e \u003cp\u003e3.3.2 Multiline Towed Arrays 33\u003c\/p\u003e \u003cp\u003e3.4 Rectangular Planar Array 33\u003c\/p\u003e \u003cp\u003e3.5 Amplitude Shading 37\u003c\/p\u003e \u003cp\u003e3.6 Continuous Arrays 37\u003c\/p\u003e \u003cp\u003e3.7 Volumetric Arrays 41\u003c\/p\u003e \u003cp\u003e3.8 Product Theorem 44\u003c\/p\u003e \u003cp\u003e3.9 Broadband Beam Patterns 45\u003c\/p\u003e \u003cp\u003e3.10 Directivity and Array Gain 45\u003c\/p\u003e \u003cp\u003e3.11 Noise Cross-Correlation between Hydrophones 47\u003c\/p\u003e \u003cp\u003e3.12 Directivity of Line Arrays 49\u003c\/p\u003e \u003cp\u003e3.13 Directivity of Area Arrays 51\u003c\/p\u003e \u003cp\u003e3.14 Directivity of Volumetric Arrays 52\u003c\/p\u003e \u003cp\u003e3.15 Difference Arrays 54\u003c\/p\u003e \u003cp\u003e3.16 Multiplicative Arrays 57\u003c\/p\u003e \u003cp\u003e3.17 Sparsely Populated Arrays 59\u003c\/p\u003e \u003cp\u003e3.18 Adaptive Beamforming 60\u003c\/p\u003e \u003cp\u003eReferences 62\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Active Sonar Sources 63\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Source Level 63\u003c\/p\u003e \u003cp\u003e4.2 Cavitation 64\u003c\/p\u003e \u003cp\u003e4.3 Near-Field Interactions 67\u003c\/p\u003e \u003cp\u003e4.4 Explosive Sources 67\u003c\/p\u003e \u003cp\u003e4.5 Physics of Shock Waves in Water 68\u003c\/p\u003e \u003cp\u003e4.6 Bubble Pulses 72\u003c\/p\u003e \u003cp\u003e4.7 Pros and Cons of Explosive Charges 73\u003c\/p\u003e \u003cp\u003e4.8 Parametric Acoustic Sources 73\u003c\/p\u003e \u003cp\u003eReferences 74\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Transmission Loss 75\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Sound Speed Profile in the Sea 76\u003c\/p\u003e \u003cp\u003e5.2 Snell’s Law and Transmission across an Interface 77\u003c\/p\u003e \u003cp\u003e5.3 Reflection and Transmission Coefficients 79\u003c\/p\u003e \u003cp\u003e5.4 Transmission through a Plate 82\u003c\/p\u003e \u003cp\u003e5.5 Ray Tracing 84\u003c\/p\u003e \u003cp\u003e5.6 Spreading Loss 91\u003c\/p\u003e \u003cp\u003e5.7 Absorption of Sound in the Ocean 92\u003c\/p\u003e \u003cp\u003e5.7.1 Mechanisms of Absorption 92\u003c\/p\u003e \u003cp\u003eReferences 95\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Transmission Loss: Interaction with Boundaries 97\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Sea State, Wind Speed, and Wave Height 97\u003c\/p\u003e \u003cp\u003e6.2 Pierson–Moskowitz Model for Fully Developed Seas 99\u003c\/p\u003e \u003cp\u003e6.3 Sea Surface Interaction 101\u003c\/p\u003e \u003cp\u003e6.3.1 Lloyd Mirror Interference 101\u003c\/p\u003e \u003cp\u003e6.3.2 Loss Due to Interaction with the Surface 104\u003c\/p\u003e \u003cp\u003e6.4 Bottom Loss 112\u003c\/p\u003e \u003cp\u003e6.4.1 Simple Rayleigh Bottom Loss Model 113\u003c\/p\u003e \u003cp\u003e6.4.2 U.S. Navy OAML Approved Models of Bottom Loss 113\u003c\/p\u003e \u003cp\u003e6.4.3 Low-Frequency Bottom Loss (LFBL) Model: 50 to 1000 Hz 113\u003c\/p\u003e \u003cp\u003e6.4.4 High-Frequency Bottom Loss (HFBL) Model 114\u003c\/p\u003e \u003cp\u003e6.4.5 High-Frequency Environment Acoustic (HFEVA) Model 117\u003c\/p\u003e \u003cp\u003e6.5 Leakage Out of a Duct, Low-Frequency Cutoff 117\u003c\/p\u003e \u003cp\u003e6.6 Propagation Loss Model Descriptions 120\u003c\/p\u003e \u003cp\u003e6.6.1 Ray Models 120\u003c\/p\u003e \u003cp\u003e6.6.2 Normal Modes 121\u003c\/p\u003e \u003cp\u003e6.6.3 Parabolic Equations 122\u003c\/p\u003e \u003cp\u003e6.6.4 U.S. Navy Standard Models 123\u003c\/p\u003e \u003cp\u003eReferences 125\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Ambient Noise 127\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Ambient Noise Models 127\u003c\/p\u003e \u003cp\u003e7.2 Seismic Noise 128\u003c\/p\u003e \u003cp\u003e7.3 Ocean Turbulence 130\u003c\/p\u003e \u003cp\u003e7.4 Shipping Noise 131\u003c\/p\u003e \u003cp\u003e7.5 Wave Noise 131\u003c\/p\u003e \u003cp\u003e7.6 Thermal Noise 131\u003c\/p\u003e \u003cp\u003e7.7 Rain Noise 131\u003c\/p\u003e \u003cp\u003e7.8 Temporal Variability of Ambient Noise 133\u003c\/p\u003e \u003cp\u003e7.9 Depth Effects on Noise 133\u003c\/p\u003e \u003cp\u003e7.10 Directionality of Noise 133\u003c\/p\u003e \u003cp\u003e7.11 Under Ice Noise 137\u003c\/p\u003e \u003cp\u003e7.12 Spatial Coherence of Ambient Noise 138\u003c\/p\u003e \u003cp\u003eReferences 140\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Reverberation 143\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Scattering, Backscattering Strength, and Target Strength 143\u003c\/p\u003e \u003cp\u003e8.1.1 Surface and Bottom Scattering 143\u003c\/p\u003e \u003cp\u003e8.1.2 Volume Scattering 152\u003c\/p\u003e \u003cp\u003e8.1.3 Bottom Scattering 152\u003c\/p\u003e \u003cp\u003e8.1.4 Reverberation Target Strength 153\u003c\/p\u003e \u003cp\u003e8.1.5 Calculation of Reverberation for Use in the Sonar Equation 154\u003c\/p\u003e \u003cp\u003e8.1.6 Volume Reverberation Level 156\u003c\/p\u003e \u003cp\u003e8.2 Reverberation Frequency Spread and Doppler Gain Potential 157\u003c\/p\u003e \u003cp\u003e8.2.1 Power Spectral Density of a CW Pulse 159\u003c\/p\u003e \u003cp\u003e8.2.2 Environmental Frequency Spreading 161\u003c\/p\u003e \u003cp\u003e8.2.3 Frequency Spreading Due to Transmitter and Receiver Motion 161\u003c\/p\u003e \u003cp\u003e8.2.4 Frequency Spreading Due to Target 162\u003c\/p\u003e \u003cp\u003e8.3 Important Observation with Respect to Reverberation 164\u003c\/p\u003e \u003cp\u003eReferences 164\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Active Target Strength 167\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Target Strength Definition 167\u003c\/p\u003e \u003cp\u003e9.2 Active Target Strength of a Large Sphere 169\u003c\/p\u003e \u003cp\u003e9.3 Active Target Strength of a Very Small Sphere 170\u003c\/p\u003e \u003cp\u003e9.4 Target Strengths of Simple Geometric Forms 173\u003c\/p\u003e \u003cp\u003e9.5 Target Strength of Submarines 173\u003c\/p\u003e \u003cp\u003e9.6 The TAP Model 174\u003c\/p\u003e \u003cp\u003e9.7 Target Strength of Surface Ships 176\u003c\/p\u003e \u003cp\u003e9.8 Target Strength of Mines and Torpedoes 176\u003c\/p\u003e \u003cp\u003e9.9 Target Strength of Fish 178\u003c\/p\u003e \u003cp\u003eReferences 181\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Radiated Noise 183\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 General Characteristics of Ship Radiated Noise 183\u003c\/p\u003e \u003cp\u003e10.2 Propeller Radiated Noise 184\u003c\/p\u003e \u003cp\u003e10.3 Machinery Noise 186\u003c\/p\u003e \u003cp\u003e10.4 Resonance Noise 187\u003c\/p\u003e \u003cp\u003e10.5 Hydrodynamic Noise 187\u003c\/p\u003e \u003cp\u003e10.6 Platform Quieting 189\u003c\/p\u003e \u003cp\u003e10.7 Total Radiated Noise 189\u003c\/p\u003e \u003cp\u003eReference 192\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Self Noise 193\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Flow Noise 193\u003c\/p\u003e \u003cp\u003e11.2 Turbulent Noise Coherence 198\u003c\/p\u003e \u003cp\u003e11.3 Strumming Noise 199\u003c\/p\u003e \u003cp\u003eReferences 199\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Statistical Detection Theory 201\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 201\u003c\/p\u003e \u003cp\u003e12.2 Case 1: Signal Is Known Exactly 205\u003c\/p\u003e \u003cp\u003e12.2.1 Observations on Case 1 210\u003c\/p\u003e \u003cp\u003e12.3 Case 2: Signal Is White Gaussian Noise 210\u003c\/p\u003e \u003cp\u003e12.3.1 Observations on Case 2 213\u003c\/p\u003e \u003cp\u003eReferences 214\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Methodology for Calculation of the Recognition Differential 215\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Continuous Broadband Signals (PBB) 216\u003c\/p\u003e \u003cp\u003e13.1.1 PBB Step 1: Theoretical Broadband Nrd 217\u003c\/p\u003e \u003cp\u003e13.1.2 PBB Step 2: Correction for Noise Spectrum 217\u003c\/p\u003e \u003cp\u003e13.1.3 PBB Step 3: Correction for Processor Implementation 220\u003c\/p\u003e \u003cp\u003e13.1.4 PBB Step 4: Correction for Nonideal Signal Characteristics 226\u003c\/p\u003e \u003cp\u003e13.1.5 PBB Step 5: Adjustment for Additional At-Sea Losses 227\u003c\/p\u003e \u003cp\u003e13.2 Continuous Narrowband Signals (PNB) 227\u003c\/p\u003e \u003cp\u003e13.2.1 PNB Step 1: Theoretical Narrowband Nrd 229\u003c\/p\u003e \u003cp\u003e13.2.2 PNB Step 2: Correction for Noise Spectrum 230\u003c\/p\u003e \u003cp\u003e13.2.3 PNB Step 3: Correction for Processor Implementation 233\u003c\/p\u003e \u003cp\u003e13.2.4 PNB Step 4: Correction for Nonideal Signal Characteristics (Signal Is Not a Perfect Sine Wave) 239\u003c\/p\u003e \u003cp\u003e13.2.5 PNB Step 5: Adjustment for Additional At-Sea Losses 240\u003c\/p\u003e \u003cp\u003e13.2.6 Nrd Calculation Example 241\u003c\/p\u003e \u003cp\u003e13.3 Active Sonar 241\u003c\/p\u003e \u003cp\u003e13.3.1 CW Active Pulse Active Step 1: Theoretical Nrd 242\u003c\/p\u003e \u003cp\u003e13.3.2 Active Step 2: Correction for Noise Spectrum 253\u003c\/p\u003e \u003cp\u003e13.3.3 Active Step 3: Correction for Processor Implementation 255\u003c\/p\u003e \u003cp\u003e13.3.4 Active Step 4: Correction for Nonideal Signal Characteristics 257\u003c\/p\u003e \u003cp\u003e13.3.5 Active Step 5: Adjustment for Additional At-Sea Losses 257\u003c\/p\u003e \u003cp\u003e13.3.6 Nrd Calculation Examples 258\u003c\/p\u003e \u003cp\u003e13.4 Aural Detection 258\u003c\/p\u003e \u003cp\u003e13.5 Display Nomenclature 261\u003c\/p\u003e \u003cp\u003eReferences 264\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 False Alarms, False Contacts, and False Targets 265\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Sea Story 265\u003c\/p\u003e \u003cp\u003e14.2 Failure to Detect 266\u003c\/p\u003e \u003cp\u003e14.3 Detection Theory 266\u003c\/p\u003e \u003cp\u003e14.3.1 Hypothesis Testing 266\u003c\/p\u003e \u003cp\u003e14.3.2 Probability Density Function 267\u003c\/p\u003e \u003cp\u003e14.3.3 Detection of Constant Level 268\u003c\/p\u003e \u003cp\u003e14.4 False Alarm Probability Calculation 269\u003c\/p\u003e \u003cp\u003e14.5 False\/Nonthreat Contacts 271\u003c\/p\u003e \u003cp\u003e14.6 False Targets 271\u003c\/p\u003e \u003cp\u003e14.7 Summary and Conclusions 272\u003c\/p\u003e \u003cp\u003eReferences 272\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Variability and Uncertainty 273\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Random Variability of a Sonar 276\u003c\/p\u003e \u003cp\u003e15.2 Sources of Variability 276\u003c\/p\u003e \u003cp\u003eReferences 281\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Modeling Detection and Tactical Decision Aids 283\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Figure of Merit Range or R50 % 283\u003c\/p\u003e \u003cp\u003e16.2 Tactical Decision Aids 287\u003c\/p\u003e \u003cp\u003eReferences 289\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Cumulative Probability of Detection 291\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 Why is CPD Important? 291\u003c\/p\u003e \u003cp\u003e17.2 Discrete Glimpse and Continuous Looking 291\u003c\/p\u003e \u003cp\u003e17.3 Lambda–Sigma Jump Model 292\u003c\/p\u003e \u003cp\u003e17.4 Nonjump Processes 293\u003c\/p\u003e \u003cp\u003e17.5 What Are Appropriate Random Parameters? 293\u003c\/p\u003e \u003cp\u003e17.6 Approximation Method for Computation of the Cumulative Probability of Detection (CPD) 296\u003c\/p\u003e \u003cp\u003eReferences 298\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Tracking, Target Motion Analysis, and Localization 299\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 Bearing Trackers 299\u003c\/p\u003e \u003cp\u003e18.1.1 Amplitude Difference Method 299\u003c\/p\u003e \u003cp\u003e18.1.2 Phase Difference Method or Cross-Correlation Method 300\u003c\/p\u003e \u003cp\u003e18.2 General Principle of Tracking and Bearing Measurement 301\u003c\/p\u003e \u003cp\u003e18.3 Other Sources of Bearing Error for Area Arrays 303\u003c\/p\u003e \u003cp\u003e18.4 Additional Sources of Errors for Line Arrays 305\u003c\/p\u003e \u003cp\u003e18.5 Bottom Bounce 306\u003c\/p\u003e \u003cp\u003e18.6 Manual versus Automatic Tracking 306\u003c\/p\u003e \u003cp\u003e18.7 Localization and Target Motion Analysis 307\u003c\/p\u003e \u003cp\u003e18.7.1 Localization 307\u003c\/p\u003e \u003cp\u003e18.7.2 Wave Front Curvature Ranging (WFCR) 312\u003c\/p\u003e \u003cp\u003e18.7.3 Multipath Ranging (MPR) 314\u003c\/p\u003e \u003cp\u003e18.7.4 Depression\/Elevation (D\/E) Ranging 317\u003c\/p\u003e \u003cp\u003e18.7.5 Triangulation Ranging 317\u003c\/p\u003e \u003cp\u003e18.8 Bearings Only Methodologies 319\u003c\/p\u003e \u003cp\u003e18.9 Four-Bearing TMA 319\u003c\/p\u003e \u003cp\u003e18.10 Ekelund Ranging 321\u003c\/p\u003e \u003cp\u003e18.11 Range and Bearing TMA 322\u003c\/p\u003e \u003cp\u003e18.12 Other Bearings Only TMA Methodologies 323\u003c\/p\u003e \u003cp\u003e18.13 Other TMA and Localization Schemes 324\u003c\/p\u003e \u003cp\u003eReferences 324\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Design and Evaluation of Sonars 325\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e19.1 Choice of Frequency and Size 325\u003c\/p\u003e \u003cp\u003e19.2 Computational Requirements 327\u003c\/p\u003e \u003cp\u003e19.2.1 Beamforming 328\u003c\/p\u003e \u003cp\u003e19.3 Signal Processing after Beamformer 329\u003c\/p\u003e \u003cp\u003e19.3.1 Detection 329\u003c\/p\u003e \u003cp\u003e19.4 Active Pulse Choice 330\u003c\/p\u003e \u003cp\u003e19.5 Monostatic, Bistatic, and Multistatic Active Sonars 332\u003c\/p\u003e \u003cp\u003e19.6 Ambiguity Functions 334\u003c\/p\u003e \u003cp\u003e19.7 Mine Hunting and Bottom Survey Sonars 334\u003c\/p\u003e \u003cp\u003e19.8 Echo Sounding and Fishing Sonars 335\u003c\/p\u003e \u003cp\u003e19.9 Navigation 336\u003c\/p\u003e \u003cp\u003e19.10 Vehicle Location and At-Sea Rescue 336\u003c\/p\u003e \u003cp\u003e19.11 Intercept Receivers 336\u003c\/p\u003e \u003cp\u003e19.12 Communications 336\u003c\/p\u003e \u003cp\u003e19.13 Marine Mammals and Active Sonar 337\u003c\/p\u003e \u003cp\u003eReferences 337\u003c\/p\u003e \u003cp\u003eA Fourier Transforms 339\u003c\/p\u003e \u003cp\u003eA.1 Definitions 339\u003c\/p\u003e \u003cp\u003eA.2 Parseval’s Theorem and Plancherel’s Theorem 340\u003c\/p\u003e \u003cp\u003eA.3 Properties of Fourier Transforms 341\u003c\/p\u003e \u003cp\u003eA.4 Localization or Uncertainty Property 341\u003c\/p\u003e \u003cp\u003eB Analysis of Errors Associated with a Least Squares Methodology 343\u003c\/p\u003e \u003cp\u003eReference 346\u003c\/p\u003e \u003cp\u003eIndex 347\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Electronics \u0026amp; communications engineering [\u003ca title=\"See our other books on Electronics \u0026amp; communications engineering\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Electronics%20\u0026amp;%20communications%20engineering%20%5BTJ%5D%22\"\u003eTJ\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley","offers":[{"title":"Brand New","offer_id":52165738463512,"sku":"9780470688755","price":106.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9780470688755.jpg?v=1781099963","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/underwater-acoustics-analysis-design-and-performance-of-sonar-hardback-9780470688755","provider":"Freshly Printed Books","version":"1.0","type":"link"}