信号的DFT对其CFT逼近程度的研究

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

Study on Signal DFT Approximation to Its CFT

Discrete Fourier Transform (DFT) or its Fast Fourier Transform (FFT) is one of most useful tools for signal analysis and processing. Suppose that signal duration is T, and 1/T is defined as fundamental frequency,an integer times of the fundamental frequency is called an integer frequency. Since signal DFT uses N integer frequency components to approach the values of its Continuous Fourier Transform (CFT) at the N integer frequencies, the DFT is usually approximate. The expression of relation between signal DFT and its CFT is derived, Based on this expression, the approximation by signal DFT to its CFT is analyzed, and a method is proposed for precisely estimating the spectrum of signals with integer and noninteger frequencies. In addition, the effects are discussed of window function shape and of adding zeroes behind data on estimating signal spectrum using DFT.