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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。
Frequency domain calculations often require interpolation. The paper points out three kinds of situations: one is that it can not operate without interpolation; the second one is to make the result of frequency domain transform to the time domain have the correct result; the other one is to move the sample point in the frequency domain Shift) requires frequency-domain interpolation in order to ensure accuracy. The numerical example illustrates the necessity of interpolation. There are three methods for frequency-domain interpolation: the first one is performed before Fourier transform, that is, the zero-point sample is added in the real-time domain; the second one is performed in Fourier transform, that is, the frequency domain is encrypted in the discrete Fourier transform; Fourier transform after. The first two methods have been widely adopted. This paper mainly discusses the third method and derives the frequency-domain interpolation function, whose form is different from the interpolation function in time domain.