论文标题
分数傅立叶变换的身份和vermor变换
Identities of the Fractional Fourier Transform and the Versor Transform
论文作者
论文摘要
我们提供了分数傅立叶变换$ \ MATHCAL {f}_θ$的介绍，并在IT和单位复数数字$ e^{iθ} $之间绘制连接。由此激励，我们定义了一个与任何单位Quaternion $ e^{iξ_{1}} \cosη+e^{iξ_{2}} j \sinη$关联的全新对象，我们称之为versor transform $ \ nathcal {v}这种转换具有傅立叶和拉普拉斯作为特殊情况的变换，鼓励对它们之间的关系有另一种看法。我们还为$ \ Mathcal {f}_θ$和$ \ Mathcal {V} _ {（ξ_{1}，η，η，η，ξ_{2}）} $得出了几个身份。
We provide an introduction to the Fractional Fourier Transform $\mathcal{F}_θ$ and draw a connection between it and the unit complex number $e^{iθ}$. Motivated by this, we define an entirely new object associated with any unit quaternion $e^{iξ_{1}}\cosη+e^{iξ_{2}}j\sinη$, which we call the Versor Transform $\mathcal{V}_{(ξ_{1},η,ξ_{2})}$. This transform, which has both the Fourier and Laplace Transforms as special cases, encourages an alternate view of the relationship between them. We also derive several identities for both $\mathcal{F}_θ$ and $\mathcal{V}_{(ξ_{1},η,ξ_{2})}$.
