Eigenvector and Fractionalization of Discrete Hadamard Transform

Author

Tseng, C.-C.

Author_Institution

Dept. of Comput. & Commun. Eng., Nat. Kaohsiung First Univ. of Sci. & Technol.

fYear

2007

Firstpage

2307

Lastpage

2310

Abstract

In this paper, the eigenvector and fractionalization of discrete Hadamard transform (DHT) is investigated. First, a Kronecker product method for finding eigenvalue and eigenvector of DHT matrix is described. Then, the number of sign change of eigenvector is used to arrange the index of eigenvector. Next, a discrete fractional Hadamard transform is defined by using the result of eigen-decomposition. Finally, the comparison with conventional recursive computation method is made to demonstrate the effectiveness of the proposed method.

Keywords

Hadamard matrices; Hadamard transforms; discrete transforms; eigenvalues and eigenfunctions; recursive estimation; Kronecker product; discrete Hadamard transform matrix; discrete fractional Hadamard transform; eigen-decomposition; eigenvalue and eigenvector; fractionalization; recursive computation; Digital signal processing; Discrete Fourier transforms; Discrete cosine transforms; Discrete transforms; Eigenvalues and eigenfunctions; Fourier transforms; Image coding; Interpolation; Karhunen-Loeve transforms; Symmetric matrices;

fLanguage

English

Publisher

ieee

Conference_Titel

Circuits and Systems, 2007. ISCAS 2007. IEEE International Symposium on

Print_ISBN

1-4244-0920-9

Electronic_ISBN

1-4244-0921-7

Type

conf

DOI

10.1109/ISCAS.2007.378849

Filename

4253136