Average densities of frequency bands of wavelets

Zhihua Zhang ()
Additional contact information
Zhihua Zhang: Beijing Normal University

Indian Journal of Pure and Applied Mathematics, 2014, vol. 45, issue 2, 199-212

Abstract: Abstract A function is called a wavelet if its integral translations and dyadic dilations form an orthonormal basis for L 2(ℝ). The support of the Fourier transform of a wavelet is called its frequency band. In this paper, we study the relation between diameters and measures of frequency bands of wavelets, precisely say, we study the ratio of the measure to the diameter. This reflects the average density of the frequency band of a wavelet. In particular, for multiresolution analysis (MRA) wavelets, we do further research. First, we discuss the relation between diameters and measures of frequency bands of scaling functions. Next, we discuss the relation between frequency bands of wavelets and the corresponding scaling functions. Finally, we give the precise estimate of the measure of frequency bands of wavelets. At the same time, we find that when the diameters of frequency bands tend to infinity, the average densities tend to zero.

Keywords: Wavelet Analysis; frequency band; average density (search for similar items in EconPapers)
Date: 2014
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13226-014-0059-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:indpam:v:45:y:2014:i:2:d:10.1007_s13226-014-0059-6

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/13226

DOI: 10.1007/s13226-014-0059-6

Access Statistics for this article

Indian Journal of Pure and Applied Mathematics is currently edited by Nidhi Chandhoke

More articles in Indian Journal of Pure and Applied Mathematics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().