Natural-ordered complex Hadamard transform
Ng, Boon Poh
Date of Issue2009
School of Electrical and Electronic Engineering
This paper presents a new transform known as natural-ordered complex Hadamard transform (NCHT) which is derived from the Walsh–Hadamard transform (WHT) through the direct block matrix operation. Some of its properties, including the exponential property of the NCHT and the shift invariant property of the NCHT power spectrum, are presented. The relationship of the NCHT with the sequency-ordered complex Hadamard transform (SCHT) is discussed. In fact, it is shown that NCHT is a natural-ordered version of complex Hadamard transform whereas SCHT shows the sequency ordering. This is parallel to their real-valued counterparts, the WHT and the sequency-ordered Walsh transform (SOWT). A fast algorithm for computing the NCHT is also developed using sparse matrix factorization and its computational complexity is examined.
DRNTU::Engineering::Electrical and electronic engineering::Electronic systems::Signal processing
© 2009 Elsevier. This is the author created version of a work that has been peer reviewed and accepted for publication by Signal Processing, Elsevier. It incorporates referee's comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [DOI: http://dx.doi.org/10.1016/j.sigpro.2009.09.007].