A Kind Of Windowed Quaternionic Linear Canonical Transform

The proposed the quaternionic linear canonical transform(QLCT)combined the quaternions with the linear canonical transform(LCT),is drawing many re-searchers' attention.It is not local but global.This paper,in order to overcome this drawback,based on the quaternionic linear canonical transform(QLCT),proposes the windowed quaternionic linear canonical transform(WQLCT),studies their properties and the uncertainty principle.The main work of this thesis can be summarized as fol-lows:(1)It introduces the basic knowledge of the quaternion and the linear canonical trans-form(LCT).Based on the existed one-dimensional linear canonical transform,this part introduces the two-dimensional linear canonical transform.(2)Based on the relationship between the quaternion and the linear canonical trans-form(LCT),it introduces the two-sided quaternionic linear canonical transform(two-sided QLCT)and the left-sided quaternionic linear canonical transform(left-sided QLCT),discussing about their properties,such as Plancherel theorem and the partial derivative properties.(3)Starting with the relationship between the quaternionic linear canonical trans-form(QLCT)and windowed fourier transform(WFT),it defines three types of WQLCT:the two-sided windowed quaternionic linear canonical transform(two-sided WQLCT),the left-sided quaternionic linear canonical transform(left-sided WQLCT)and the right-sided quaternionic linear canonical transform(right-sided WQLCT).In the part of the two-sided WQLCT and the left-sided WQLCT,in or-der to reflect their inner product form,it defines a new atomic operator.