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Wavelet analysis and signal processing. (English) Zbl 0792.94004
Ruskai, Mary Beth (ed.) et al., Wavelets and their applications. Boston, MA etc.: Jones and Bartlett Publishers. 153-178 (1992).
The authors define the concept of “libraries”, structures relating to different time scales at different times (or different spatial scales at different locations), with the aim of realizing the basis in which a given signal can be most efficiently superposed in terms of oscillatory modes on different time scales. This also provides an efficient compression method. The authors discuss two principal libraries, namely trigonometric waveform libraries (which are localized sine transforms) and the wavelet packet library (which contains the wavelet basis, Walsh functions and smooth versions of Walsh functions called wavelet packets). They give a simple characterization of subsets forming orthonormal bases and some examples of specific computations using their process.
For the entire collection see [Zbl 0782.00087].
Reviewer: J.S.Joel (Kelly)

MSC:
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
65T99 Numerical methods in Fourier analysis
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