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离散傅立叶变换（ＤＦＴ）或它的快速计算（ＦＦＴ）是信号分析与处理最有力的工具之一，但由于它是用为基频整数倍的Ｎ个频率分量去逼近实际信号的连续傅立叶变换（ＣＦＴ）的值，故用ＤＦＴ估计信号的频谱通常是近似的．本文不仅给出了信号的ＤＦＴ与其ＣＦＴ之间的关系式，而且在此基础上证明了用ＤＦＴ估计信号谱的近似性，给出了用ＤＦＴ精确估计整数频率和非整数频率信号的频谱方法．同时，还研究了窗函数的形状及在离散数据后面补零对用ＤＦＴ估计这些信号ＣＦＴ的影响
Discrete Fourier Transform (DFT) or its fast computation (FFT) is one of the most powerful tools for signal analysis and processing, but since it is a continuous Fourier transform that approximates the actual signal using N frequency components that are integral multiples of the fundamental frequency CFT) value, so using DFT to estimate the frequency spectrum of the signal is usually approximate. This paper not only gives the relation between the signal DFT and its CFT, but also proves the approximation of the signal spectrum by DFT, and gives the spectrum method of accurately estimating the integer frequency and non-integer frequency signals by DFT. At the same time, we also study the shape of the window function and zero-padding the discrete data to estimate the influence of these signals CFT by DFT