Relationship between Discrete Fourier Transformation and Eigenvalue Decomposition

Abstract

Abstract-Discrete Fourier transformation (DFT) of sample sequence and eigenvalue decomposition of sample correlation matrix are two of important tools and basic parts in signal and information processing. Since they are used to deal with the same random process, although from different viewpoint, there may be some intrinsic relationship between them. However, they are often introduced, explained and learned independently in the traditional textbooks and courses of signal and information processing. Here, we discuss some intrinsic relationship between the problems formulation of discrete Fourier transformation of sample sequence and eigenvalue decomposition of sample correlation matrix. The results of these lecture notes can help students deepen the understanding of their characteristics on simplicity, optimality and the reason why they are so popular and why we analyze and deal with signal and information processing by using discrete Fourier transformation of sample sequence and eigenvalue decomposition of sample correlation matrix. He is an associate professor with the Department of Electronic Engineering, UESTC. His research interests include array signal processing, engineering applications of geometric algebra and hyper complex.Jihao Yin received the Ph.D. degree in electrical engineering