Uncertainty principles in linear canonical domains. Issue 1 (2nd January 2021)

• Record Type: Journal Article
• Authors: Lian, Pan
• Is Part Of: Integral transforms and special functions. Volume 32:Issue 1(2021)
• Page Start: 67
• Page End: 77
• Publication Date: 2021-01-02
• Subjects: Linear canonical transform -- uncertainty principle -- measurable sets; 42A38 -- 94A12; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2020.1795845
• Languages: English
• ISSNs: 1065-2469

Abstract

Abstract : The linear canonical transform has been found various applications in several areas, such as signal processing and optics. Several uncertainty principles were established for this transform in the last years. However, most results only focused on the uncertainty relations in two different time-frequency domains. In this paper, we study the uncertainty principle for measurable sets associated with several different linear canonical domains. We first give uncertainty relations for three different linear domains and then generalize it to n different linear canonical domains. It is shown that the new lower bound is tighter than the classical result, in some special cases.