UM  > 科技學院  > 數學系
Time-frequency aspects of nonlinear fourier atoms
Chen Q.1; Li L.1; Qian T.2
Subtype
2007
PublisherBirkhäuser Basel
Publication PlaceBasel
Abstract

In the standard Fourier analysis one uses the linear Fourier atoms {e: n ∈ ℤ}. With only the linear phases nt Fourier analysis can not expose the essence of time-varying frequencies of nonlinear and non-stationary signals. In this note we study time-frequency properties of a new family of atoms e: n ∈ ℤ, non-linear Fourier atoms, where a is any but fixed complex number with |a| < 1, and dθ(t) a harmonic measure on the unit circle parameterized by t. The nonlinear Fourier atoms {e: n ∈ ℤ} were first noted in [12] with some examples and theoretically studied in [8]. In this note we show that the real parts cos θ(t), |a| < 1, form a family of intrinsic mode functions introduced in the HHT theory [5]. We prove that for a fixed a the set {e: n ∈ ℤ}, constitutes a Riesz basis in the space L([0, 2π]). Some miscellaneous results including Shannon type sampling theorems are obtained.

KeywordHilbert-huang Transform Nonlinear Fourier Atom Sampling Theorem Time-frequency Analysis
ISBN978-3-7643-7777-9
DOI10.1007/978-3-7643-7778-6_22
URLView the original
Pages287-297
Language英语
Fulltext Access
Citation statistics
Cited Times [WOS]:4   [WOS Record]     [Related Records in WOS]
Document TypeBook
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.Faculty of Mathematics and Computer Science,Hubei University,Wuhan,P. R. China
2.Department of Mathematics Faculty of Science and Technology,University of Macau,Macao (via Hong Kong)
Recommended Citation
GB/T 7714
Chen Q.,Li L.,Qian T.. Time-frequency aspects of nonlinear fourier atoms[M]. Basel:Birkhäuser Basel,2007.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Chen Q.]'s Articles
[Li L.]'s Articles
[Qian T.]'s Articles
Baidu academic
Similar articles in Baidu academic
[Chen Q.]'s Articles
[Li L.]'s Articles
[Qian T.]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Chen Q.]'s Articles
[Li L.]'s Articles
[Qian T.]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.
 

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.