Wavelets provide a new tool for the analysis of vibration records. They allow the changing spectral composition of a nonstationary signal to be measured and presented in the form of a time-frequency map. The purpose of this paper, which is Part 1 of a pair, is to introduce and review the theory of orthogonal wavelets and their application to signal analysis. It includes the theory of dilation wavelets, which have been developed over a period of about ten years, and of harmonic wavelets which have been proposed recently by the author. Part II is about presenting the results on wavelet maps and gives a selection of examples. The papers will interest those who work in the field of vibration measurement and analysis and who are in positions where it is necessary to understand and interpret vibration data.

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