Part I Sonar and underwater acoustics 1 Introduction to underwater acoustic signal processing . 3 1.1 Overview of underwater acoustic signal processing . 3 1.1.1 Common applications . 5 1.1.

2 Signal and information processing . 6 1.1.3 Underwater acoustic system and signal processing examples . 7 1.1.4 Development process for novel applications . 7 1.

2 Intended use and organization of this book . 8 References . 11 2 Sonar systems and the sonar equation . 13 2.1 Introduction . 13 2.2 Remote sensing with sonar systems . 13 2.

2.1 Components of a sonar system . 14 2.2.2 Monostatic, bistatic, and distributed sonar systems . 16 2.2.3 Estimating position of a sound or scattering source: localization .

17 2.2.4 Bistatic active sonar . 24 2.2.5 Doppler scale and shift . 27 2.2.

6 Doppler sensitive and insensitive waveforms . 33 2.3 The sonar equation . 34 2.3.1 Decibel notation . 36 2.3.

2 The basic passive sonar equation . 39 2.3.3 The basic active sonar equation . 45 2.3.4 Summary of sonar equation terms . 51 2.

3.5 Relating SNR to detection performance: Detection Threshold . 52 2.3.6 Relating SNR to estimation performance . 62 2.3.7 Other applications of the sonar equation .

64 References . 69 3 Underwater acoustics . 71 3.1 Introduction . 71 3.2 Acoustic propagation in the ocean . 71 3.2.

1 Acoustic pressure, particle velocity, intensity, power, and energy density . 73 3.2.2 The wave equation and spherical waves . 77 3.2.3 Periodic signals, wavelength, and wavenumber . 80 3.

2.4 Cylindrical spreading and plane waves . 82 3.2.5 Nearfield and farfield propagation . 84 3.2.6 Inhomogeneous wave equation and the channel impulse response .

86 3.2.7 The Helmholtz equation and channel frequency response . 89 3.2.8 Source level and transmission loss . 90 3.2.

9 Absorption and dispersion . 94 3.2.10 Sound-speed, Snell''s law, and refraction . 95 3.2.11 Boundaries and reflection loss . 101 3.

2.12 Rays and modes in shallow water . 116 3.2.13 Reciprocity . 124 3.3 Ambient noise . 126 3.

3.1 Overview and ambient noise spectrum curves . 126 3.3.2 Very low frequency . 128 3.3.3 Low frequency: Distant shipping noise .

129 3.3.4 Low to high frequency: Wind-related surface noise . 130 3.3.5 Very high frequency: Thermal noise . 131 3.3.

6 Spatio-temporal and statistical properties of ambient noise . 132 3.4 Scattering from objects: Target echoes and target strength . 132 3.4.1 Target strength . 133 3.4.

2 Target impulse response . 136 3.4.3 Scattering from objects: the ka dependence . 139 3.5 Reverberation . 148 3.5.

1 Sources of reverberation . 148 3.5.2 Volume reverberation . 149 3.5.3 Boundary reverberation . 153 3.

5.4 Signal to reverberation ratio . 156 3.5.5 Statistical characterization of reverberation . 156 3.5.6 Spectral properties of reverberation .

158 3.5.7 Reverberation from a moving source . 159 References . 163 Part II Systems, signal processing and mathematical statistics background 4 Linear systems and signal processing . 169 4.1 Introduction . 169 4.

2 Linear-time-invariant (LTI) systems and convolution . 169 4.2.1 Impulse response of an LTI system . 170 4.2.2 Frequency response of an LTI system . 173 4.

3 Fourier transforms . 174 4.3.1 Inverse Fourier transform. 175 4.3.2 Properties of the Fourier transform . 176 4.

4 Hilbert transform. 181 4.5 Signal time-bandwidth product . 182 4.6 Converting analog signals to digital signals . 184 4.6.1 Sampling and aliasing .

185 4.6.2 Quantization. 187 4.7 Discrete-time signals and systems . 190 4.7.1 Fourier transform of a discrete-time signal .

191 4.7.2 Properties of the Fourier transform of discrete-time signals . 192 4.8 Discrete and fast Fourier transforms (DFT and FFT) . 193 4.9 Discrete-time filtering (LPF, HPF, and BPF) . 196 4.

9.1 FIR and IIR filters . 197 4.9.2 FIR filter design . 199 4.9.3 Band-pass and high-pass filters .

201 4.9.4 FIR filter implementation . 202 4.10 Windowing and window functions . 203 4.10.1 Rectangular, uniform, or boxcar window .

207 4.10.2 Tukey window . 208 4.10.3 Hamming window . 208 4.10.

4 Taylor window . 209 4.10.5 Kaiser window . 210 4.10.6 Hann window . 210 4.

10.7 Blackman window . 211 4.11 Decimation and interpolation . 212 References . 215 5 Mathematical statistics . 217 5.1 Introduction .