解析频域抽样时对应的时域信号失真

Analysis the Distortion of Time Signal When Sampling in Frequency Domain

根据频域抽样定理可知 ,如果序列 x( n)的长度为 M,则只有当频域抽样点数 N M时 ,才可以由频域抽样序列 XN( k)经离散傅里叶反变换恢复原始序列 x( n) ,否则将会产生时域信号失真。频域抽样点数 N越少 ,时域信号失真越严重。本文从理论上具体分析了当序列较长而实际频域抽样点数较少时 。

According to the sampling theorem of frequency domain, if the length of x(n) is M, Only when N, which is the sampling number in frequency domain, is more than M or equal to M, can x(n) be reconstructed without distortion. Otherwise, the distortion phenomenon will happen. The less the length is, the worse the distortion will be. The distortion phenomenon in time domain during sampling in frequency domain is analyzed detailedly in this paper, when the length of sequence is far longer than the sampling number in frequency domain.