Uncertainty principles in linear canonical domains

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-frequ...

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Bibliographic Details
Published in:Integral transforms and special functions 2021-01, Vol.32 (1), p.67-77
Main Author: Lian, Pan
Format: Article
Language:English
Subjects:
Linear canonical transform
Lower bounds
measurable sets
Principles
Signal processing
uncertainty principle
Uncertainty principles
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Summary: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.
ISSN:1065-2469
1476-8291
DOI:10.1080/10652469.2020.1795845