Wavelets: a passing wave or a truly useful tool?

Wavelets are a new family of signal transformations. In a wavelet transform, the signal is decomposed in terms of dilates and translates of a single function, the mother wavelet. Wavelet transforms have a number of properties that can be exploited in many signal processing applications. These properties include an ability to trade time and frequency resolutions in a controlled manner, a relationship between the time behavior of a signal and the structure of its wavelet transform and compact representations for wide classes of deterministic and stochastic signals. This paper provides an overview of continuous and discrete wavelet transforms and reviews some of their applications.