离散傅里叶变换的对角化
On the diagonalization of the discrete Fourier transform
摘要：
离散傅里叶变换（DFT）是作用在环Z/NZ上复值函数的Hilbert空间上的一种重要算子。在N=p是奇素数的情况下，我们展示了DFT的特征向量的规范基。从标准基到规范基的转移矩阵定义了一种新的变换，我们称之为离散振子变换（简称DOT）。最后，我们描述了一个快速算法计算离散振子变换在某些情况下。
英文摘要：
The discrete Fourier transform (DFT) is an important operator which acts on the Hilbert space of complex valued functions on the ring Z/NZ. In the case where N=p is an odd prime number, we exhibit a canonical basis of eigenvectors for the DFT. The transition matrix from the standard basis to the canonical basis defines a novel transform which we call the discrete oscillator transform (DOT for short). Finally, we describe a fast algorithm for computing the discrete oscillator transform in certain cases.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
