Details

Autor(en) / Beteiligte

• Hu, Xiaoxiao
• Cheng, Dong
• Kou, Kit Ian

Titel

Convolution theorems associated with quaternion linear canonical transform and applications

Ist Teil von

• Signal processing, 2023-01, Vol.202, p.108743, Article 108743

Ort / Verlag

Elsevier B.V

Erscheinungsjahr

2023

Link zum Volltext

Quelle

Elsevier ScienceDirect Journals Complete

Beschreibungen/Notizen

• •Novel types of convolution operators for quaternion linear canonical transform are proposed. Type one and two are defined in the spatial and spectral domains, respectively.•They are distinct in the quaternion space and are consistent once in complex or real space.•Their applications are the solution of the Fredholm integral equation of the first kind involving special kernels, some special systems of second-order partial differential equations, and the design of multiplicative filters. Novel types of convolution operators for quaternion linear canonical transform (QLCT) are proposed. Type one and two are defined in the spatial and QLCT spectral domains, respectively. They are distinct in the quaternion space and are consistent once in complex or real space. Various types of convolution formulas are discussed. Consequently, the QLCT of the convolution of two quaternionic functions can be implemented by the product of their QLCTs, or the summation of the products of their QLCTs. As applications, correlation operators and theorems of the QLCT are derived. The proposed convolution formulas are used to solve Fredholm integral equations with special kernels. Some systems of second-order partial differential equations, which can be transformed into the second-order quaternion partial differential equations, can be solved by the convolution formulas as well. As a final point, we demonstrate that the convolution theorem facilitates the design of multiplicative filters.