有限域上的无穷序列、级数收敛和离散时间傅里叶变换
Infinite Sequences, Series Convergence and the Discrete Time Fourier Transform over Finite Fields
摘要：
数字变换在信道编码、密码学和数字信号处理等学科中有重要的应用。本文研究了两种傅里叶变换：离散时间傅里叶变换（DTFT）和有限域傅里叶变换（FFFT）。介绍了DTFT的有限域形式，并利用复核重新定义了FFFT，使其成为离散傅里叶变换的更合适的有限域形式。这些变换可以处理有限代数结构上定义的FIR和IIR滤波器。
英文摘要：
Digital Transforms have important applications on subjects such as channel coding, cryptography and digital signal processing. In this paper, two Fourier Transforms are considered, the discrete time Fourier transform (DTFT) and the finite field Fourier transform (FFFT). A finite field version of the DTFT is introduced and the FFFT is redefined with a complex kernel, which makes it a more appropriate finite field version of the Discrete Fourier Transform. These transforms can handle FIR and IIR filters defined over finite algebraic structures.
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。
