The Haar wavelet representation and a number of related representations have been shown to be a simple and powerful technique for similarity matching of time series. In this report, we extend the standard formulation to the translation invariant oversampled system. This makes possible a particularly efficient incremental scheme for coefficient calculation. As an additional benefit, the oversampled scheme provides for easy incremental update of the decomposition on new input samples. The system is further extended over higher order scaling functions of smoother character and over wavelets with more vanishing moments.

MODELS AND PRINCIPLES (acm H.1), PATTERN RECOGNITION (acm I.5), MISCELLANEOUS (acm J.m), PHYSICAL SCIENCES AND ENGINEERING (acm J.2), DATA STORAGE REPRESENTATIONS (acm E.2)
Fractals (msc 28A80), Probabilistic methods, simulation and stochastic differential equations (msc 65Cxx), Stochastic differential and integral equations (msc 65C30), Computational Markov chains (msc 65C40), Other computational problems in probability (msc 65C50), Computational problems in statistics (msc 65C60), Pattern recognition, speech recognition (msc 68T10), Searching and sorting (msc 68P10)
Information (theme 2)
CWI
Information Systems [INS]
Database Architectures

Struzik, Z.R. (2001). Oversampling the Haar wavelet transform. Information Systems [INS]. CWI.