A wavelet-based algorithm for the Hilbert transform

In this paper, a Hilbert transform algorithm is developed based on an analysing wavelet. It has a nice feature that one level of combination wavelet forms an orthogonal filter. As a result, a perfect orthogonality and constant passband are obtained. Meanwhile it solves the problem of selectivity for a passband width by construction of the combination wavelet. Some properties of the proposed algorithm are illustrated in detail by examples. The proposed algorithm has also been used as a tool for signal analysis, especially in extracting orthogonality modulated signals from a mechanical dynamic system. (C) 1996 Academic Press Limited