A Study of Asymptotically Optimal Time-frequency Localization by Scaling Functions and Wavelets
Charles K. Chui, Jianzhong Wang · 2000
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 caling funciotn is a finite symmetric P'olya frequency sequence. The main result in this paper is that stoplets and cowlets are asymptotical Gaussians and modulated Gaussians, respectively, and provide asymptotically optmal (i.e. smallest) time-frequency lowpass and bandpass windows.