Uncertainty products of local periodic wavelets
نویسندگان
چکیده
This paper is on the angle-frequency localization of periodic scaling functions and wavelets. It is shown that the uncertainty products of uniformly local, uniformly regular and uniformly stable scaling functions and wavelets are uniformly bounded from above by a constant. Results for the construction of such scaling functions and wavelets are also obtained. As an illustration, scaling functions and wavelets associated with a family of generalized periodic splines are studied. This family is generated by periodic weighted convolutions, and it includes the well-known periodic B-splines and trigonometric B-splines.
منابع مشابه
Trigonometric Wavelets and the Uncertainty Principle
The time-frequency localization of trigonometric wavelets is discussed. A good measure is provided by a periodic version of the Heisenberg uncertainty principle. We consider multiresolution analyses generated by de la Vall ee Poussin means of the Dirichlet kernel. For the resulting interpolatory and orthonormal scaling functions and wavelets, the uncertainty product can be bounded from above by...
متن کاملTime Frequency Localization of Trigonometric Hermite Operators
In this paper, localization properties of trigonometric polynomial Hermite operators are discussed. In particular, time frequency uncertainty and operator norms are compared for the diierent types of fundamental interpolants which serve as scaling functions for a trigono-metric multiresolution analysis. x1. Introduction Recently, several diierent approaches to periodic multiresolution analyses ...
متن کاملKernels of Spherical Harmonics and Spherical Frames
Our concern is with the construction of a frame in L 2 (S) consisting of smooth functions based on kernels of spherical harmonics. The corresponding decomposition and reconstruction algorithms utilize discrete spherical Fourier transforms. Numerical examples connrm the theoretical expectations. x1. Introduction Traditionally, wavelets were tailored to problems on the Euclidean space IR d. Howev...
متن کاملWavelets Associated with Periodic Basis
In this paper, we investigate a class of nonstationary, orthogonal, periodic scaling functions and wavelets generated by continuously diier-entiable periodic functions with positive Fourier coeecients; such functions are termed periodic basis functions. For this class of wavelets, the decomposition and reconstruction coeecients can be computed in terms of the discrete Fourier transform, so that...
متن کاملOptimally Localized Wavelets and Smoothing Kernels
It is well-known that the Gaussian functions and, more generally, their modulations-translations (the Gabor functions) have the unique property of being optimally localized in space and frequency in the sense of Heisenberg’s uncertainty principle. In this thesis, we address the construction of complex wavelets modeled on the Gabor function, and smoothing kernels based on the Gaussian. We procee...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Adv. Comput. Math.
دوره 13 شماره
صفحات -
تاریخ انتشار 2000