Sequency-Ordered Complex Hadamard Transform: Properties, Computational Complexity and Applications

Author

Aung, Aye ; Ng, Boon Poh ; Rahardja, Susanto

Author_Institution

Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore

Volume

56

Issue

8

fYear

2008

Firstpage

3562

Lastpage

3571

Abstract

In this paper, the generation of sequency-ordered complex Hadamard transform (SCHT) based on the complex Rademacher matrices is presented. The exponential form of SCHT is also derived, and the proof for the unitary property of SCHT is given. Using the sparse matrix factorization, the fast and efficient algorithm to compute the SCHT transform is developed, and its computation load is described. Certain properties of the SCHT matrices are derived and analyzed with the discussion of SCHT applications in spectrum analysis and image watermarking. Relations of SCHT with fast Fourier transform (FFT) and unified complex Hadamard transform (UCHT) are discussed.

Keywords

Hadamard matrices; Hadamard transforms; computational complexity; fast Fourier transforms; image coding; sparse matrices; spectral analysis; watermarking; FFT; Rademacher matrix; SCHT; computational complexity; fast Fourier transform; image watermarking; sequency-ordered complex Hadamard transform; sparse matrix factorization; spectrum analysis; Computational complexity; Digital signal processing; Discrete cosine transforms; Discrete transforms; Error correction; Error correction codes; Image analysis; Image coding; Signal processing algorithms; Sparse matrices; Complex Hadamard transforms; discrete orthogonal transforms; fast algorithms; sequency-ordered complex Hadamard transform (SCHT);

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/TSP.2008.923195

Filename

4567635