Abstract
The success of discrete wavelet methods for pattern matching applications can be significantly increased by finding a wavelet that closely approximates the pattern of interest. However, the process of fitting a wavelet to a given pattern is non-linear and non-trivial. In this paper we will address two problems. First, we develop and analyze an analytic approach for constructing a family of discrete wavelets that is optimally fitted to a given pattern. The construction is based on computing a suitable lifting filter. Secondly, we apply this matched wavelet approach to detect defects in linear guideways. Results with real data from acoustic measurements of such defects illustrate the potential of this approach.
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