一种基于神经网络的离散傅里叶矩阵重构方法研究  

Reseach on a reconstruction method of discrete Fourier matrix based on neural network

作　　者：黄权 阮建高 HUANG Quan;RUAN Jiangao(The Fifth Electronics Research Institute of the Ministry of Industry Information Technology,Guangzhou 510610,China)

机构地区：[1]工业和信息化部电子第五研究所,广东广州510610

出　　处：《电子设计工程》2022年第16期1-5,共5页Electronic Design Engineering

基　　金：国家自然科学基金(62001123)。

摘　　要：傅里叶变换是一种经典的信号分析方法,在计算机上实现傅里叶变换时,需要构建离散傅里叶矩阵,再与离散信号进行矩阵乘法,由于离散傅里叶矩阵包含复数,因此傅里叶变换的过程涉及复数运算。为了避开复数运算,文中提出了一种离散傅里叶矩阵的构造方法,通过该方法构造的矩阵不包含复数,但仍然保留着和原始离散傅里叶矩阵同样的信息;通过神经网络学习离散傅里叶矩阵,并进行对比分析,实验结果表明,神经网络可以很好地学习离散傅里叶矩阵,并基于此矩阵重构出信号。Fourier transform is a classical signal analysis method.It is necessary to construct the discrete Fourier matrix when implementing the Fourier transform in computer,then the transform is performed by the product of the discrete Fourier matrix and the desired signal.Fourier transform contains arithmetic operation of complex numbers due to that discrete Fourier matrix consists of complex numbers.In order to avoid complex number operation,this paper proposes a reconstruction method of discrete Fourier matrix.The method perfectly avoids complex number while retaining all the information from the original matrix;A neural network is designed to learn the discrete Fourier matrix,and comparison and analysis are made.The experiments show that neural network can perfectly learn the discrete Fourier matrix by which reconstructs signal.

关 键 词：离散傅里叶矩阵 神经网络 信号重构 数字信号处理 

分 类 号：TN91[电子电信—通信与信息系统] TP3[电子电信—信息与通信工程]