## An Introduction to Random Vibrations, Spectral and Wavelet AnalysisThis book is a substantially expanded edition of An Introduction to Random Vibrations and Spectral Analysis which now covers wavelet analysis. Basic theory is thoroughly described and illustrated, with a detailed explanation of how discrete wavelet transforms work. Computer algorithms are expalined and supported by examples and set of problems. An appendix lists 10 computer programs for calculating and displaying wavelet transforms. |

### Contents

Joint probability distributions ensemble averages | 12 |

3 | 21 |

Fourier analysis | 41 |

Copyright | |

26 other sections not shown

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### Common terms and phrases

a₁ algorithm aliasing amplitude analysis approximately assume autocorrelation function bandwidth binary signal c₁ calculated Chapter circular correlation complex consider constant correlation function corresponding cross-spectral density defined delta functions DFT's discrete Fourier transform discrete wavelet transform E[y² ensemble average equation ergodic example excitation filter Fourier series frequency response function function x(t Gaussian given gives Hence input integral inverse linear system mean square mean value measured N₁ N₂ narrow band process noise obtain one-dimensional orthogonal output periodic Prob probability density function probability distribution problem rad/s random process x(t random variable random vibration Rayleigh distribution result sample functions sampling interval scaling function sequence shown in Fig spectral coefficients spectral density spectral estimates spectral window spectrum stationary process substituting summation t₁ w₁ w₂ wavelet transform X₁ x₁(t x₂ y₁ zero Δω Σ Σ