| Preface to the first edition | p. ix |
| Preface to the second edition | p. xi |
| Preface to the third edition | p. xii |
| Acknowledgements | p. xiv |
| List of symbols | p. xvii |
| Introduction to probability distributions and averages | p. 1 |
| Probability density function | p. 2 |
| Gaussian distribution | p. 7 |
| Calculation of averages | p. 7 |
| Probability distribution function | p. 10 |
| Joint probability distributions, ensemble averages | p. 12 |
| Second-order probability functions | p. 12 |
| Second-order averages | p. 14 |
| Conditional probability | p. 17 |
| Second-order Gaussian distribution | p. 18 |
| Ensemble averaging | p. 19 |
| Correlation | p. 21 |
| Autocorrelation | p. 25 |
| Cross-correlation | p. 29 |
| Fourier analysis | p. 33 |
| Fourier integral | p. 35 |
| Complex form of the Fourier transform | p. 38 |
| Spectral density | p. 41 |
| Narrow band and broad band processes | p. 44 |
| Spectral density of a derived process | p. 46 |
| Cross-spectral density | p. 48 |
| Note on the units of spectral density | p. 51 |
| Excitation - response relations for linear systems | p. 53 |
| Classical approach | p. 54 |
| Frequency response method | p. 55 |
| Impulse response method | p. 58 |
| Relationship between the frequency response and impulse response functions | p. 60 |
| Calculation of response to an arbitrary input | p. 62 |
| Transmission of random vibration | p. 67 |
| Mean level | p. 68 |
| Autocorrelation | p. 69 |
| Spectral density | p. 71 |
| Mean square response | p. 73 |
| Cross-correlation | p. 77 |
| Cross-spectral density | p. 78 |
| Probability distributions | p. 79 |
| Statistics of narrow band processes | p. 82 |
| Crossing analysis | p. 85 |
| Distribution of peaks | p. 90 |
| Frequency of maxima | p. 92 |
| Accuracy of measurements | p. 95 |
| Analogue spectrum analysis | p. 96 |
| Variance of the measurement | p. 97 |
| Analysis of finite length records | p. 103 |
| Confidence limits | p. 108 |
| Digital spectral analysis I: Discrete Fourier transforms | p. 113 |
| Discrete Fourier transforms | p. 114 |
| Fourier transforms of periodic functions | p. 116 |
| Aliasing | p. 118 |
| Calculation of spectral estimates | p. 120 |
| Digital spectral analysis II: Windows and smoothing | p. 125 |
| Relationship between linear and circular correlation | p. 126 |
| Fourier transform of a train of aperiodic functions | p. 129 |
| Basic lag and spectral windows | p. 131 |
| Smoothing spectral estimates | p. 137 |
| Extending record length by adding zeros | p. 139 |
| Summary | p. 142 |
| Practical considerations | p. 146 |
| The fast Fourier transform | p. 150 |
| Basic theory | p. 150 |
| Sample calculation | p. 152 |
| Programming flow charts | p. 155 |
| Practical value of FFT | p. 162 |
| Alternative algorithms | p. 165 |
| Pseudo random processes | p. 167 |
| Random binary process | p. 168 |
| Pseudo random binary signals | p. 172 |
| Random multi-level process | p. 175 |
| Spectrum of a multi-level process | p. 179 |
| Generation of random numbers | p. 183 |
| Synthesis of correlated noise sources | p. 185 |
| Application notes | p. 189 |
| Response of a resonant mode to broad band excitation | p. 189 |
| Fatigue and failure due to random vibration | p. 191 |
| Excitation by random surface irregularities | p. 196 |
| Simulation of random environments | p. 201 |
| Frequency response function and coherency measurements | p. 206 |
| Local spectral density calculations | p. 218 |
| Weibull distribution of peaks | p. 219 |
| Multi-dimensional spectral analysis | p. 225 |
| Two-dimensional Fourier series | p. 225 |
| Properties of the two-dimensional DFT | p. 229 |
| Spectral density of a multi-dimensional random process | p. 233 |
| Discrete spectral density and circular correlation functions for a two-dimensional random process | p. 239 |
| Two-dimensional windows | p. 245 |
| Two-dimensional smoothing | p. 254 |
| Artificial generation of a two-dimensional random process | p. 256 |
| Generation of an isotropic surface | p. 258 |
| Cross-spectral density between parallel tracks across a random surface | p. 263 |
| Response of continuous linear systems to stationary random excitation | p. 268 |
| Response to excitation applied at a point | p. 268 |
| Response to distributed excitation | p. 277 |
| Normal mode analysis | p. 280 |
| Kinetic energy of a flat plate subjected to uncorrelated random excitation | p. 290 |
| Single degree-of-freedom analogy | p. 292 |
| Discrete wavelet analysis | p. 295 |
| Basic ideas | p. 295 |
| Dilation equations | p. 300 |
| Dilation wavelets | p. 303 |
| Properties of the wavelet coefficients | p. 307 |
| Circular wavelet transforms | p. 322 |
| Discrete wavelet transforms | p. 326 |
| Properties of the DWT | p. 339 |
| Mean-square maps | p. 348 |
| Convolution by wavelets | p. 353 |
| Two-dimensional wavelet transforms | p. 355 |
| Harmonic wavelets | p. 359 |
| Discrete harmonic wavelet transform | p. 364 |
| Concluding comments | p. 370 |
| Appendices | |
| Table of integrals | p. 371 |
| Computer programs | p. 373 |
| The Gaussian probability integral | p. 379 |
| Distribution of x[superscript 2 subscript k] | p. 381 |
| Random numbers | p. 383 |
| Distribution of reverse arrangements for a random series | p. 385 |
| Wavelet programs | p. 387 |
| Problems | p. 401 |
| Answers to problems | p. 457 |
| References | p. 465 |
| Table of Contents provided by Ingram. All Rights Reserved. |
