摘要
本文从矩阵群的观点出发讨论了分数Ｆｏｕｒｉｅｒ变换的数学描述并通过数字仿真直观地说明了它进行信号时－频分析的两个特点。结果表明，在矩阵描述下，经典的Ｆｏｕｒｉｅｒ变换相当于一个置换矩阵：一般的分数Ｆｏｕｒｉｅｒ变换相当于一个广义置换矩阵；分数Ｆｏｕｒｉｅｒ变换全体构成的变换族可以用一个矩阵群来描述，多次变换运算完全转化为相应的矩阵乘法运算。最后，数字信号分数Ｆｏｕｒｉｅｒ变换的仿真计算表明，分数Ｆｏｕｒｉｅｒ变换具有独特的时－频分析性质。
In this paper, by using the matrix group,we study the mathematical representation of the fractional Fourier transform (FRFT), and simulating show the two specific properties of time-frequency analysis of signal with FRFT directly. Our results are that. a classical Fourier transform(FT) operator to a permutation matrix(PM), a FRFT operator corresponds to a special general permutation matrix(GPM), the FRFT operator group correspond to a special general permutation matrix group(GPMG), and multiple transform operator equal to a matrix multiplication. Finally numerical simulation of FRFT of signal show that FRFT has special properties of time-frequency analysis for the signal processing
出处
《信号处理》
CSCD
2001年第2期162-167,129,共7页
Journal of Signal Processing
