频域插值问题

频域运算中往往需要插值。文中指出了三种情况:一种是不插值就不能运算;第二种是为了使频域运算结果变换到时域时能有正确的结果;再一种就是频域中样点移动(例如偏移)时为了保证精度需要频域插值。本文用数值例子说明了插值的必要性。频域插值有三种方法:第一种在傅氏变换之前进行,即时域补充零值样点;第二种在傅氏变换中进行,即离散傅氏变换中加密频域间隔;第三种在傅氏变换之后进行。前两种方法已得到广泛采用。本文主要讨论第三种方法,导出了频域插值函数,它的形式与时域插值函数有所不同。

Interpolation in frequency domain

Interpolation is often required in tlie operation of frequency domain.The paper lists three cases where.interpolation is necessary:case I.operation can not be done without interpolation;case 2.frequency domain computation result being transformed into time domain.interpolation leads to correct result;case 3.interpolation is necessary for ensuring the migration accz}racy in frequency domain.There aret'nree methods of frequency domain interpolation.the first method is employed before Fouriertransform.i.e.replenishing zero samples in time domain;the second method is performed during Fourier transform.i.e.densifying sample points of frequency domain in discrete Fourier transform;the third method is done after Fourier transform.The former two are already in wide use.This paper concentrates on the third method.and derives the function of frequency domain interpolation.the form of which is difrerent from that of time domain interpolation function.