| Preface to the first edition |
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ix | |
| Preface to the second edition |
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xi | |
| Preface to the third edition |
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xii | |
| Acknowledgements |
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xiv | |
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xvii | |
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Introduction to probability distributions and averages |
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1 | (11) |
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Probability density function |
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2 | (5) |
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7 | (1) |
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7 | (3) |
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Probability distribution function |
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10 | (2) |
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Joint probability distributions, ensemble averages |
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12 | (9) |
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Second-order probability functions |
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12 | (2) |
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14 | (3) |
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17 | (1) |
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Second-order Gaussian distribution |
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18 | (1) |
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19 | (2) |
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21 | (12) |
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25 | (4) |
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29 | (4) |
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33 | (8) |
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35 | (3) |
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Complex form of the Fourier transform |
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38 | (3) |
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41 | (12) |
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Narrow band and broad band processes |
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44 | (2) |
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Spectral density of a derived process |
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46 | (2) |
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48 | (3) |
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Note on the units of spectral density |
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51 | (2) |
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Excitation - response relations for linear systems |
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53 | (14) |
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54 | (1) |
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Frequency response method |
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55 | (3) |
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58 | (2) |
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Relationship between the frequency response and impulse response functions |
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60 | (2) |
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Calculation of response to an arbitrary input |
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62 | (5) |
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Transmission of random vibration |
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67 | (15) |
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68 | (1) |
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69 | (2) |
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71 | (2) |
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73 | (4) |
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77 | (1) |
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78 | (1) |
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Probability distributions |
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79 | (3) |
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Statistics of narrow band processes |
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82 | (13) |
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85 | (5) |
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90 | (2) |
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92 | (3) |
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95 | (18) |
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Analogue spectrum analysis |
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96 | (1) |
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Variance of the measurement |
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97 | (6) |
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Analysis of finite length records |
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103 | (5) |
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108 | (5) |
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Digital spectral analysis I: Discrete Fourier transforms |
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113 | (12) |
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Discrete Fourier transforms |
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114 | (2) |
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Fourier transforms of periodic functions |
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116 | (2) |
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118 | (2) |
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Calculation of spectral estimates |
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120 | (5) |
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Digital spectral analysis II: Windows and smoothing |
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125 | (25) |
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Relationship between linear and circular correlation |
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126 | (3) |
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Fourier transform of a train of aperiodic functions |
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129 | (2) |
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Basic lag and spectral windows |
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131 | (6) |
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Smoothing spectral estimates |
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137 | (2) |
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Extending record length by adding zeros |
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139 | (3) |
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142 | (4) |
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146 | (4) |
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The fast Fourier transform |
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150 | (17) |
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150 | (2) |
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152 | (3) |
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155 | (7) |
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162 | (3) |
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165 | (2) |
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167 | (22) |
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168 | (4) |
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Pseudo random binary signals |
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172 | (3) |
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Random multi-level process |
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175 | (4) |
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Spectrum of a multi-level process |
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179 | (4) |
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Generation of random numbers |
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183 | (2) |
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Synthesis of correlated noise sources |
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185 | (4) |
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189 | (36) |
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Response of a resonant mode to broad band excitation |
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189 | (2) |
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Fatigue and failure due to random vibration |
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191 | (5) |
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Excitation by random surface irregularities |
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196 | (5) |
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Simulation of random environments |
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201 | (5) |
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Frequency response function and coherency measurements |
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206 | (12) |
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Local spectral density calculations |
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218 | (1) |
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Weibull distribution of peaks |
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219 | (6) |
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Multi-dimensional spectral analysis |
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225 | (43) |
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Two-dimensional Fourier series |
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225 | (4) |
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Properties of the two-dimensional DFT |
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229 | (4) |
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Spectral density of a multi-dimensional random process |
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233 | (6) |
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Discrete spectral density and circular correlation functions for a two-dimensional random process |
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239 | (6) |
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245 | (9) |
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Two-dimensional smoothing |
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254 | (2) |
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Artificial generation of a two-dimensional random process |
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256 | (2) |
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Generation of an isotropic surface |
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258 | (5) |
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Cross-spectral density between parallel tracks across a random surface |
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263 | (5) |
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Response of continuous linear systems to stationary random excitation |
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268 | (27) |
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Response to excitation applied at a point |
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268 | (9) |
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Response to distributed excitation |
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277 | (3) |
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280 | (10) |
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Kinetic energy of a flat plate subjected to uncorrelated random excitation |
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290 | (2) |
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Single degree-of-freedom analogy |
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292 | (3) |
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Discrete wavelet analysis |
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295 | (106) |
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295 | (5) |
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300 | (3) |
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303 | (4) |
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Properties of the wavelet coefficients |
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307 | (15) |
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Circular wavelet transforms |
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322 | (4) |
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Discrete wavelet transforms |
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326 | (13) |
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339 | (9) |
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348 | (5) |
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353 | (2) |
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Two-dimensional wavelet transforms |
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355 | (4) |
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359 | (5) |
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Discrete harmonic wavelet transform |
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364 | (6) |
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370 | (1) |
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Appendix 1 Table of integrals |
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371 | (2) |
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Appendix 2 Computer programs |
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373 | (6) |
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Appendix 3 The Gaussian probability integral |
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379 | (2) |
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Appendix 4 Distribution of Χ2k |
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381 | (2) |
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Appendix 5 Random numbers |
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383 | (2) |
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Appendix 6 Distribution of reverse arrangements for a random series |
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385 | (2) |
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Appendix 7 Wavelet programs |
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387 | (14) |
| Problems |
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401 | (56) |
| Answers to problems |
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457 | (8) |
| References |
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465 | (7) |
| Index |
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472 | |
