Circuits Syst Signal Process https://doi.org/10.1007/s00034-018-0863-z Uncertainty Principles for the Offset Linear Canonical Transform Haiye Huo Received: 26 October 2017 / Revised: 24 May 2018 / Accepted: 25 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract The offset linear canonical transform (OLCT) provides a more general framework for a number of well-known linear integral transforms in signal processing and optics, such as Fourier transform, fractional Fourier transform, linear canonical transform. In this paper, to characterize simultaneous localization of a signal and its OLCT, we extend some different uncertainty principles (UPs), including Nazarov’s UP, Hardy’s UP, Beurling’s UP, logarithmic UP and entropic UP, which have already been well studied in the Fourier transform domain over the last few decades, to the OLCT domain in a broader sense. Keywords Offset linear canonical transform · Uncertainty principle · Logarithmic uncertainty estimate · Entropic inequality · Localization 1 Introduction Uncertainty principle (UP) plays an important role in quantum mechanics  and signal processing . In quantum mechanics, UP was ﬁrst proposed by the German physicist W. Heisenberg in 1927 . It basically says that the more precisely the position of a particle is determined, the less precisely its momentum
Circuits, Systems and Signal Processing – Springer Journals
Published: Jun 4, 2018
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