对离散Hilbert变换的补充

A Supplementary to the Discrete Hilbert Transform

本文旨在对[3]中认为 u+(n)的博氏变换不存在这一事实展开对 u+(n)广义傅氏变换的讨论.文中严格地证明了 u+(n)的广义傅氏变换是存在的,并有其封闭的解析式.在此基础上所推导的离散的 Hilbert 变换与其连续形式完全一致.

This paper is intended to start a discussion on the viewpoint in〔3〕 which maintains the Fourier transfor of discrete signal u_+(n)to be non-existent. Also,the paper provides a rigorous justification which proves that the Fourier transform of u_+(n)not only is existent but also possesses a closed analytical ex- pression.As a result of his derivation,the discrete Hilbert transform becomes a complete counterpart of the continuous case.