DocumentCode :
929987
Title :
Matrix decomposition and butterfly diagrams for mutual relations between Hadamard-Haar and arithmetic spectra
Author :
Falkowski, Bogdan J. ; Yan, Shixing
Author_Institution :
Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore
Volume :
53
Issue :
5
fYear :
2006
fDate :
5/1/2006 12:00:00 AM
Firstpage :
1119
Lastpage :
1129
Abstract :
The mutual relationships between Hadamard-Haar and Arithmetic transforms and their corresponding spectra in the form of matrix decomposition as layered vertical and horizontal Kronecker matrices are discussed here together with their proofs, fast algorithms, and computational costs. The new relations apply to an arbitrary dimension of the transform matrices and allow performing direct conversions between Arithmetic and Hadamard-Haar functions and their corresponding spectra. In addition, analysis of butterfly diagrams for these new relations is also introduced and it is shown that they are more efficient than the matrix decomposition method.
Keywords :
Haar transforms; Hadamard transforms; matrix decomposition; Haar transforms; Hadamard transforms; Kronecker matrices; arithmetic transforms; butterfly diagrams; matrix decomposition; Arithmetic; Circuit testing; Discrete Fourier transforms; Discrete transforms; Electronic design automation and methodology; Error correction; Error correction codes; Fourier transforms; Matrix decomposition; Pattern recognition; Arithmetic transform; Hadamard–Haar transform; discrete transforms; fast transforms; spectral techniques;
fLanguage :
English
Journal_Title :
Circuits and Systems I: Regular Papers, IEEE Transactions on
Publisher :
ieee
ISSN :
1549-8328
Type :
jour
DOI :
10.1109/TCSI.2006.869899
Filename :
1629250
Link To Document :
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