Generalized Discretization of Continuous-Time Distributions
Generalized Discretization of Continuous-Time Distributions
复制标题
连续时间分布的广义离散化
DOI：
10.1049/joe.2019.1124
复制
发表时间：
2020
期刊：
影响因子：
--
通讯作者：
S. Kawai and N. Hori
中科院分区：
文献类型：
--
作者：
上原日和;松尾保孝;合谷賢治;西島喜明;安原亮;上原日和;村上政直;小西大介;S. Kawai and N. Hori
在这项研究中，最近为连续时间分布提出的离散化定义不仅适用于普通函数，而且适用于包括弱导数在内的各种分布，以便在有用的定理下从统一的角度看待它们。虽然不是绝对有必要为具有有限值的离散时间信号引入分布，但事实证明，引入离散时间等价物来欣赏其丰富性是有见地的，当采样间隔接近零时，其最终成为连续时间分布。例如，分布的导数的离散化可以被发现为分布的离散化的离散导数。这比传统的方法要容易得多，在传统的方法中，必须首先找到一个普通的函数来近似分布的导数。仿真结果表明，通过改变该模型的单个参数，可以得到与传统的Dirichlet核函数、高斯分布函数和sinc近似函数分别近似分布所得到的信号相似的不同类型的信号。
In this study, the definition of discretisation that was proposed recently for continuous‐time distributions is made applicable not only to ordinary functions but to a variety of distributions including weak derivatives such that they could be viewed from a unified perspective under useful theorems. While it is not absolutely necessary to introduce distributions for discrete‐time signals having finite values, it turns out that it is insightful to introduce discrete‐time equivalents in appreciating their richness, which culminates into continuous‐time distributions as the sampling‐interval approaches zero. For instance, a discretisation of a derivative of a distribution can be found as a discrete derivative of a discretisation of a distribution. This is much easier than the traditional approach, where an ordinary function must first be found to approximate the derivative of a distribution. Simulations show that, by changing a single parameter of the proposed model, different types of signals that are similar to traditional ones developed separately by approximating distributions by ordinary functions, such as Dirichlet’ kernel, Gaussian distribution and sinc approximation, can be obtained.