Chui, C. K.; Wang, J. Z. A study of asymptotically optimal time-frequency localization by scaling functions and wavelets. (English) Zbl 0883.42030 Ann. Numer. Math. 4, No. 1-4, 193-216 (1997). 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. Cited in 10 Documents MSC: 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems 94A12 Signal theory (characterization, reconstruction, filtering, etc.) Keywords:stoplets; cowlets; Pólya frequency sequence; asymptotical Gaussians; modulated Gaussians; time-frequency lowpass and bandpass windows PDFBibTeX XMLCite \textit{C. K. Chui} and \textit{J. Z. Wang}, Ann. Numer. Math. 4, No. 1--4, 193--216 (1997; Zbl 0883.42030)