Oversampling the Haar wavelet transform

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.