a review of the various fields of wavelet applications

Over the last decade or so, wavelets have had a growing impact on signal processing theory and practice, both because of their unifying role and their successes in applications. filter banks, which lie at the heart of wavelet-based algorithms, have become standard signal processing operators, used routinely in applications ranging from compression to modems. the contributions of wavelets have often been in the subtle interplay between discrete-time and continuous-time signal processing. the purpose of this article is to look at recent wavelet advances from a signal processing perspective. in particular, approximation results are reviewed, and the implication on compression algorithms is discussed. new constructions and open problems are also addressed.