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| Preface to the first edition | |
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| Preface to the second edition | |
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| Preface to the third edition | |
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| Acknowledgements | |
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| List of symbols | |
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| Introduction to probability distributions and averages | |
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| Probability density function | |
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| Gaussian distribution | |
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| Calculation of averages | |
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| Probability distribution function | |
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| Joint probability distributions, ensemble averages | |
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| Second-order probability functions | |
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| Second-order averages | |
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| Conditional probability | |
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| Second-order Gaussian distribution | |
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| Ensemble averaging | |
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| Correlation | |
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| Autocorrelation | |
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| Cross-correlation | |
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| Fourier analysis | |
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| Fourier integral | |
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| Complex form of the Fourier transform | |
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| Spectral density | |
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| Narrow band and broad band processes | |
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| Spectral density of a derived process | |
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| Cross-spectral density | |
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| Note on the units of spectral density | |
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| Excitation - response relations for linear systems | |
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| Classical approach | |
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| Frequency response method | |
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| Impulse response method | |
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| Relationship between the frequency response and impulse response functions | |
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| Calculation of response to an arbitrary input | |
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| Transmission of random vibration | |
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| Mean level | |
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| Autocorrelation | |
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| Spectral density | |
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| Mean square response | |
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| Cross-correlation | |
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| Cross-spectral density | |
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| Probability distributions | |
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| Statistics of narrow band processes | |
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| Crossing analysis | |
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| Distribution of peaks | |
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| Frequency of maxima | |
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| Accuracy of measurements | |
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| Analogue spectrum analysis | |
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| Variance of the measurement | |
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| Analysis of finite length records | |
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| Confidence limits | |
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| Digital spectral analysis I: Discrete Fourier transforms | |
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| Discrete Fourier transforms | |
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| Fourier transforms of periodic functions | |
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| Aliasing | |
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| Calculation of spectral estimates | |
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| Digital spectral analysis II: Windows and smoothing | |
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| Relationship between linear and circular correlation | |
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| Fourier transform of a train of aperiodic functions | |
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| Basic lag and spectral windows | |
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| Smoothing spectral estimates | |
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| Extending record length by adding zeros | |
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| Summary | |
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| Practical considerations | |
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| The fast Fourier transform | |
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| Basic theory | |
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| Sample calculation | |
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| Programming flow charts | |
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| Practical value of FFT | |
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| Alternative algorithms | |
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| Pseudo random processes | |
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| Random binary process | |
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| Pseudo random binary signals | |
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| Random multi-level process | |
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| Spectrum of a multi-level process | |
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| Generation of random numbers | |
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| Synthesis of correlated noise sources | |
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| Application notes | |
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| Response of a resonant mode to broad band excitation | |
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| Fatigue and failure due to random vibration | |
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| Excitation by random surface irregularities | |
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| Simulation of random environments | |
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| Frequency response function and coherency measurements | |
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| Local spectral density calculations | |
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| Weibull distribution of peaks | |
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| Multi-dimensional spectral analysis | |
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| Two-dimensional Fourier series | |
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| Properties of the two-dimensional DFT | |
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| Spectral density of a multi-dimensional random process | |
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| Discrete spectral density and circular correlation functions for a two-dimensional random process | |
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| Two-dimensional windows | |
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| Two-dimensional smoothing | |
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| Artificial generation of a two-dimensional random process | |
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| Generation of an isotropic surface | |
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| Cross-spectral density between parallel tracks across a random surface | |
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| Response of continuous linear systems to stationary random excitation | |
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| Response to excitation applied at a point | |
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| Response to distributed excitation | |
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| Normal mode analysis | |
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| Kinetic energy of a flat plate subjected to uncorrelated random excitation | |
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| Single degree-of-freedom analogy | |
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| Discrete wavelet analysis | |
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| Basic ideas | |
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| Dilation equations | |
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| Dilation wavelets | |
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| Properties of the wavelet coefficients | |
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| Circular wavelet transforms | |
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| Discrete wavelet transforms | |
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| Properties of the DWT | |
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| Mean-square maps | |
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| Convolution by wavelets | |
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| Two-dimensional wavelet transforms | |
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| Harmonic wavelets | |
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| Discrete harmonic wavelet transform | |
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| Concluding comments | |
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| Appendices | |
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| Table of integrals | |
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| Computer programs | |
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| The Gaussian probability integral | |
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| Distribution of x[superscript 2 subscript k] | |
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| Random numbers | |
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| Distribution of reverse arrangements for a random series | |
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| Wavelet programs | |
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| Problems | |
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| Answers to problems | |
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| References | |