Wavelets, adapted waveforms and de-noising

This is a short summary of a talk given at the Frontier Science in EEG Symposium, Continuous Waveform Analysis, held on 9 October 1993 in New Orleans. We describe some new libraries of waveforms well-adapted to various numerical analysis and signal processing tasks. The main point is that by expanding a signal in a library of waveforms which are well-localized in both time and frequency, one can achieve both understanding of structure and efficiency in computation. We briefly cover the properties of the new "wavelet packet" and "localized trigonometric" libraries. The main focus will be applications of such libraries to the analysis of complicated transient signals: a feature extraction and data compression algorithm for speech signals which uses best-adapted time and frequency decompositions, and an adapted waveform analysis algorithm for removing fish noises from hydrophone recordings. These signals share many of the same properties as EEG traces, but with distinct features that are easier to characterize and detect.