Uncertainty Principles Of Quaternion Linear Canonical Transformation

Based on the quaternion Fourier transform(QFT),this paper studies the uncertainty principle of the quaternion window Fourier transform(QWFT),the uncertainty principle of the two-sided quaternion linear canonical transform(QLCT)and the uncertainty principle of the offset quaternion linear canonical transform(OQLCT).The specific contents and conclusions are as follows.In Chapter 1,we summarize the background of the thesis,and recall the newest development of the literature.Besides,we give the related concepts and summarize the main results of this article.In Chapter 2,we consider Donoho-Stark uncertainty principle for the right-sided QWFT,Entropic uncertainty principle for the two-sided QWFT.In Chapter 3,we consider uncertainty principles for the two-sided QLCT in the sense of full space,which include logarithmic uncertainty principle,Heisenberg-type uncertainty principle,Hardy uncertainty principle,Beurling uncertainty principle and Entropic uncertainty principle.We also prove uncertainty principles for the two-sided QLCT in the sense of measurable space,including Local uncertainty principle,Benedicks-AmreinBerthier uncertainty principle and Donoho-stark uncertainty principle.The above results describe the uncertainty relationship between a quaternion signal in spatial and another quaternion signal in the frequency domain,or it can be said that the uncertainty relationship of a quaternion signal in two different QLCT domains.In addition,in order to analyze the non-stationary signal and time-varying system,we present Lieb's uncertainty principle for the two-sided short-time quaternion linear canonical transform.In Chapter 4,we propose uncertainty principles for the OQLCT in the sense of full space,which include logarithmic uncertainty principle,Heisenberg-type uncertainty principle and Entropic uncertainty principle.We also prove uncertainty principles for the two-sided OQLCT in the sense of measurable space,including Local uncertainty principle,Benedicks-Amrein-Berthier uncertainty principle and Donoho-stark uncertainty principle.The above results describe the uncertainty principle of a quaternion signal function in space and frequency domain.In addition,in order to analyze the non-stationary signal and time-varying system,we present Lieb's uncertainty principle for the short-time offset quaternion linear canonical transform.In Chapter 5,a summary of main work of the whole thesis is given and some problems to be further studied are discussed.