Compactly Supported One-cyclic Wavelets Derived from Beta Distributions
نویسندگان
چکیده
New continuous wavelets of compact support are introduced, which are related to the beta distribution. They can be built from probability distributions using ”blur”derivatives. These new wavelets have just one cycle, so they are termed unicycle wavelets. They can be viewed as a soft variety of Haar wavelets whose shape is fine-tuned by two parameters a and b. Close expressions for beta wavelets and scale functions as well as their spectra are derived. Their importance is due to the Central Limit Theorem applied for compactly supported signals. 1
منابع مشابه
On the Construction of a Class of Bidimensional Nonseparable Compactly Supported Wavelets
Chui and Wang discussed the construction of one-dimensional compactly supported wavelets under a general framework, and constructed one-dimensional compactly supported spline wavelets. In this paper, under a mild condition, the construction of M = ( 1 1 1 −1 )-wavelets is obtained.
متن کاملCompactly Supported Tight Aane Spline Frames in L 2 (ir D ) Compactly Supported Tight Aane Spline Frames in L 2 (ir D )
The theory of RS2] is applied to yield compactly supported tight aane frames (wavelets) in L 2 (IR d) from box splines. The wavelets obtained are smooth piecewise-polynomials on a simple mesh; furthermore, they exhibit a wealth of symmetries, and have a relatively small support. The number of \mother wavelets", however, increases with the increase of the required smoothness. Two bivariate const...
متن کاملStability and Independence for Multivariate Re nable Distributions
Due to their so-called time-frequency localization properties, wavelets have become a powerful tool in signal analysis and image processing. Typical constructions of wavelets depend on the stability of the shifts of an underlying re nable function. In this paper, we derive necessary and su cient conditions for the stability of the shifts of certain compactly supported re nable functions. These ...
متن کاملConstruction of compactly supported biorthogonal wavelets
This paper presents a construction of compactly supported biorthogonal spline wavelets in L2(IR ). In particular, a concrete method for the construction of bivariate compactly supported biorthogonal wavelets from box splines of increasing smoothness is provided. Several examples are given to illustrate the method. Key-Words:multivariate biorthogonal wavelets, multivariate wavelets, box splines,...
متن کامل