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A study of asymptotically optimal time-frequency localization by scaling functions and wavelets. (English) Zbl 0883.42030

Summary: The notions of stoplets and cowlets are introduced in this paper. We will call a scaling function a stoplet and its corresponding semi-orthogonal minimally supported wavelet a cowlet, if the two-scale sequence (or mask) of the scaling function is a finite symmetric Pólya frequency sequence. The main result in this paper is that stoplets and cowlets are asymptotical Gaussians and modulated Gaussians, respectively, and provide asymptotically optimal (i.e., smallest) time-frequency lowpass and bandpass windows.

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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