【摘要】 目的　研究快速傅立叶变换补零问题;方法　基于傅立叶变换定义,分析任意函数序列x(n)补零前后傅立叶变换结果;分析推导补零规则;运用同余概念及其运算规则,分析补零规则各量之间的关系。结果　任意长度的函数序列长度补零前后傅立叶变换结果是不相同的;补零必须使得补零后函数序列数N1为补零前函数序列数N的整数倍,中且为2的整数次幂;若要满足这一条件,则N必为2的整数次幂。结论　使用快速傅立叶变换算法对任意长度函数序列补零时,必须注意到补零前后傅立叶变换的结果是不相同的;若按补零规则补(r-1)N个零,则可使补零后特定关系的函数序列的傅立叶变换对应于补零前的傅立叶变换;并非任意长度的函数序列都能满足这一关系,只有N为2的整数次幂的函数序列才能满足补零规则的要求。更多还原

【Abstract】 Aim It is studied that the problem of adding zero in the algorithm of Cooley-Tukey fast Fourier transform, as the algorithm demands that the number of x（n） series must be N=2ⁿ （n is a whole number）, otherwise zero must be added to satisfy the demand. Methods Based on the definition of Fourier transform the result of Fourier transform is analyzed before and after adding zero. The rule of adding zero are analyzed and given. The relationship about the variate of equation for the rule of adding zero is also proposed. Results It is different that Fourier transform for x（n） before and after adding zero.The number of x（n） series N₁ after adding zero must be N₁=2ⁿ; Furthermore, N must be N=2ⁿ.Conclusion It is must be noticed that the result of Fourier transform is different before and after adding zero for x（n） ; When adding （r-1）N zero according the rule of adding zero, some result after adding zero is equal to the result before adding zero; Only when N is 2ⁿthe demond of adding zero rule can be satisfied.更多还原