Fast Eigenvector Algorithm for Discrete Fourier Transform and Number Theoretic Transform
Date Issued
2006
Date
2006
Author(s)
Chang, Kuo-Wei
DOI
en-US
Abstract
This dissertation is composed of three parts. The first part discusses two topics in number theory, Gauss Sum and Ramanujan Sum, respectively. We will not only research some basic properties of these Sums, but also study their applications in digital signal processing, especially in discrete Fourier Transform (DFT). Because Number Theoretic Transform (NTT) has similar traits with DFT, we will also talk about it.
The second part of this dissertation discusses the topic in the efficient bit and digital reversal algorithm, using vector calculation. The novel algorithm takes the advantage of MATLAB’s vector characteristics and can be implemented by no more than 4 lines MATLAB procedures.
Finally, we will focus on Reduced Biquaternions (RB), also called Bicomplex numbers, in the third part of this paper. There are two applications to the RB. One is array processing and the other is quaternion finite field transform. The former is related to the MUSIC algorithm; the latter is similar to complex NTT.
Subjects
數位傅立葉轉換
數論轉換
特徵向量
Discrete Fourier Transform
Number Theoretic Transform
Eigenvector
Type
thesis
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