Preface |
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ix | |
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1 Nonstationary Signals and Spectral Properties |
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1 | (18) |
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1 | (4) |
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1.2 Nonstationary Signals |
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5 | (2) |
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1.3 The Fourier Transform and the Average Properties |
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7 | (3) |
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1.4 The Analytic Signal and the Instantaneous Properties |
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10 | (3) |
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1.5 Computation of the Instantaneous Frequency |
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13 | (3) |
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1.6 Two Groups of Time-Frequency Analysis Methods |
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16 | (3) |
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19 | (28) |
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2.1 Short-time Fourier Transform |
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19 | (4) |
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23 | (3) |
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2.3 The Cosine Function Windows |
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26 | (5) |
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2.4 Spectral Leakage of Window Functions |
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31 | (2) |
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2.5 The Gabor Limit of Time-Frequency Resolution |
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33 | (3) |
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2.6 Implementation of the Gabor Transform |
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36 | (4) |
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2.7 The Inverse Gabor Transform |
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40 | (2) |
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2.8 Application in Inverse Q Filtering |
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42 | (5) |
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3 The Continuous Wavelet Transform |
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47 | (26) |
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3.1 Basics of the Continuous Wavelet Transform |
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47 | (4) |
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3.2 The Complex Morlet Wavelet |
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51 | (3) |
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3.3 The Complex Morse Wavelet |
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54 | (4) |
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3.4 The Generalised Seismic Wavelet |
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58 | (4) |
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3.5 The Pseudo-frequency Representation |
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62 | (3) |
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3.6 The Inverse Wavelet Transform |
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65 | (2) |
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3.7 Implementation of the Continuous Wavelet Transform |
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67 | (2) |
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3.8 Hydrocarbon Reservoir Characterisation |
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69 | (4) |
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73 | (22) |
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4.1 Basics of the S Transform |
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74 | (3) |
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4.2 The Generalised S Transform |
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77 | (2) |
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4.3 The Fractional Fourier Transform |
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79 | (4) |
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4.4 The Fractional S Transform |
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83 | (3) |
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4.5 Implementation of the S Transforms |
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86 | (2) |
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4.6 The Inverse S Transforms |
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88 | (5) |
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4.7 Application to Clastic and Carbonate Reservoirs |
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93 | (2) |
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95 | (22) |
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5.1 Basics of the W Transform |
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95 | (4) |
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5.2 The Generalised W Transform |
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99 | (7) |
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5.3 Implementation of Nonstationary Convolution |
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106 | (2) |
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5.4 The Inverse W Transform |
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108 | (1) |
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5.5 Application to Detecting Hydrocarbon Reservoirs |
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109 | (3) |
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5.6 Application to Detecting Karst Voids |
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112 | (5) |
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6 The Wigner--Ville Distribution |
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117 | (34) |
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6.1 Basics of the Wigner--Ville Distribution (WVD) |
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117 | (3) |
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6.2 Defining the WVD with an Analytic Signal |
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120 | (3) |
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6.3 Properties of the WVD |
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123 | (3) |
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126 | (6) |
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6.5 The Generalised Class of Time-Frequency Representations |
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132 | (2) |
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6.6 The Ambiguity Function and the Generalised WVD |
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134 | (6) |
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6.7 Implementation of the Standard and Smoothed WVDs |
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140 | (7) |
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6.8 Implementation of the Ambiguity Function and the Generalised WVD |
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147 | (4) |
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151 | (24) |
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7.1 Basics of Matching Pursuit |
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151 | (2) |
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7.2 Three-stage Matching Pursuit |
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153 | (4) |
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7.3 Matching Pursuit with the Morlet Wavelet |
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157 | (2) |
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159 | (4) |
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7.5 Multichannel Matching Pursuit |
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163 | (5) |
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7.6 Structure-adaptive Matching Pursuit |
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168 | (2) |
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170 | (5) |
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8 Local Power Spectra with Multiple Windows |
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175 | (22) |
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8.1 Multiple Orthogonal Windows |
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176 | (2) |
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8.2 Multiple Windows Defined by the Prolate Spheroidal Wavefunctions |
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178 | (2) |
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8.3 Multiple Windows Constructed by Solving a Discretised Eigenvalue Problem |
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180 | (4) |
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8.4 Multiple Windows Constructed by Gaussian Functions |
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184 | (3) |
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8.5 The Gabor Transform with Multiple Windows |
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187 | (4) |
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8.6 The WVD with Multiple Windows |
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191 | (4) |
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8.7 Prospective of Time-Frequency Analysis without Windowing |
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195 | (2) |
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197 | (22) |
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A The Gaussian Integrals, the Gamma Function, and the Gaussian Error Functions |
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197 | (3) |
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B Fourier Transforms of the Tapered Boxcar Window, the Truncated Gaussian Window, and the Weighted Cosine Window |
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200 | (3) |
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C The Generalised Seismic Wavelet in the Time Domain |
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203 | (2) |
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D Implementation of the Fractional Fourier Transform |
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205 | (1) |
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E Marginal Properties and the Analytic Signal in the WVD Definition |
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206 | (5) |
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F The Prolate Spheroidal Wavefunctions, the Associated and the Ordinary Legendre Polynomials |
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211 | (8) |
References |
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219 | (8) |
Author Index |
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227 | (2) |
Subject Index |
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229 | |