Real-time wavelet transform algorithms for the processing of continuous streams of data

Two new algorithms to compute the direct and the inverse discrete wavelet transform of continuous streams of data are discussed in this paper. The algorithms are optimized to be used in uniprocessor systems, presenting as one of their main features the ability to compute over the borders of the data segments without relying on any techniques that are traditionally used for thus task, like zero padding. A modified version of the recursive pyramid algorithm was used to compute the direct transform, keeping just the features to minimize data storage but eliminating its dependency on extension techniques. The inverse transform is computed by an algorithm inspired in the RPA, the quadrature mirror filter bank and the overlap-save method for filter convolutions. To evaluate the performance the algorithms were implemented on a DSP coupled to a digitizer through its external memory bus, what allowed deterministic behavior. After a stage of optimization an analysis of data storage and computation load were made. These results and the potential applications are discussed at the end of the paper.