论文标题
卷积定理与四元素线性规范变换和应用相关的卷积定理
Convolution theorems associated with quaternion linear canonical transform and applications
论文作者
论文摘要
提出了新型的杂音算子的卷积运算符，用于线性典型变换（QLCT）。一型和第二个分别在空间和QLCT光谱域中定义。它们在四元空间中是不同的，并且在复杂或真实空间中保持一致。讨论了各种类型的卷积公式。因此，可以通过其QLCT的乘积或QLCT的产品的汇总来实施两个四离子功能的卷积QLCT。作为应用程序，得出了QLCT的相关运算符和定理。所提出的卷积公式用于与特殊内核求解弗雷德姆积分方程。二阶偏微分方程的某些系统也可以通过卷积公式来求解为二阶季节部分微分方程。最后，我们证明了卷积定理有助于乘法过滤器的设计。
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.
