Uncertainty principle and orthogonal condition for the short-time linear canonical transform. Issue 6 (September 2016)

• Record Type: Journal Article
• Authors: Huang, Lei; Zhang, Ke; Chai, Yi; Xu, Shuiqing
• Is Part Of: Signal, image and video processing. Volume 10:Issue 6(2016)
• Page Start: 1177
• Page End: 1181
• Publication Date: 2016-09
• Subjects: Linear canonical transform -- Short-time linear canonical transform -- Uncertainty principle -- Orthogonal condition; Signal processing -- Digital techniques -- Periodicals; Image processing -- Digital techniques -- Periodicals; Digital video -- Periodicals; 621.3822
• DOI: 10.1007/s11760-016-0874-9
• Languages: English
• ISSNs: 1863-1703

Abstract

Abstract The short-time linear canonical transform (STLCT) is a novel time–frequency analysis tool, which maps the time domain signal into the joint time and frequency domain. This short paper investigates its two theoretical problems. The first one relates to the uncertainty principle in one STLCT domain, and the other one is that coefficients of the short-time linear canonical expansion (STLCE) are of incompleteness. To solve these issues, first, we develop the uncertainty principle in one STLCT domain. Second, the orthogonal condition is proposed to guarantee the completeness of the STLCE coefficients.