The circular Bedrosian identity for translation‐invariant operators: existence and characterization
Abstract
The analytic signal method via the circular Hilbert transform is a critical tool in the time–frequency analysis of signals of finite duration. The circular Bedrosian identity is of major theoretical and practical value in the method. The identity holds whenever the Fourier coefficients of f,g∈L2([−π,π]) are respectively supported on A = [−n,m] and for some non‐negative integers 0≤n,m≤+∞. In this note, we investigate the existence of such an identity for a general‐bounded linear translation‐invariant operator on L2([−π,π]d) and for general support sets . We give an insightful geometric characterization of the support sets for the existence. In addition, we find all the support sets for the partial Hilbert transforms. Copyright © 2015 John Wiley & Sons, Ltd.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Mar 16, 2015
- Source ID
- 10.1002/mma.3456
Entities
People
- Haizhang Zhang
- Rongrong Lin
- Wei Hu
Organizations
- Army Research Office
- National Natural Science Foundation of China
- Sun Yat-sen University