Abstract
Wavelets are an alternative way to partition phase space in which the frequency band is decomposed into intervals of different lengths. Since these lengths are powers of two, these intervals can be thought of as octaves. Different octaves must be sampled at different rates. A multiresolution approximation is a mathematically precise notion of just such a partitioning scheme. Wavelet bases arise from the idea of generating a mutiresolution analysis from dilates and translates of a single function. We begin with a general treatment of multiresolution analysis together with a procedure for constructing wavelet bases from such structures. An associated filtering theory, known in the engineering literature as quadrature mirror filters, is also discussed. These constructions are carried out for the various examples of multiresolution approximations. The chapter concludes with an introduction to the construction of compactly supported wavelets.
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© 1998 Springer Science+Business Media New York
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Ramanathan, J. (1998). Wavelet Analysis. In: Methods of Applied Fourier Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1756-5_9
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DOI: https://doi.org/10.1007/978-1-4612-1756-5_9
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7267-0
Online ISBN: 978-1-4612-1756-5
eBook Packages: Springer Book Archive