分数阶四元数傅立叶变换及其应用

Fractional Quaternion Fourier Transform and Its Applications

在缩减双四元数代数系统上定义了分数阶四元数傅立叶变换.这一变换可以看成是缩减双四元数傅立叶变换的推广.同时推导了分数阶四元数傅立叶变换的帕塞瓦尔定理和卷积定理,给出了分数阶四元数傅立叶变换的快速算法,最后讨论了分数阶四元数傅立叶变换域滤波器的设计.

In this paper,we define the fractional quaternion Fourier transform based on reduced biquaternion algebra.The fractional quaternion Fourier transform can be seen as the generalization of reduced biquaternion Fourier transform.Moreover,the Parseval s theorem and convolution theorem associated with fractional quaternion Fourier transform was derived.Besides,the fast algorithms of fractional quaternion Fourier transform was given.In the end,the design of multiplicative filter was proposed in this paper.