Summary form only given. Wavelets have emerged in the last decadeas a synthesis from many disciplines, ranging from pure mathematics(where forerunners were used to study singular integral operators) toelectrical engineering (quadrature mirror filters), borrowing in passingfrom quantum physics, from geophysics and from computer aided design.The author presents an overview of the ideas in wavelet theory, andshows how it fits into the different disciplines in which it is rooted.Some recent applications are discussed, including a nonlinear“squeezing” of the wavelet transform, inspired by auditorymodels, with applications to speech processing; and a discussion of thenonlinear approximation and why wavelets are so successful in thenonlinear approximation
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