NDLI: A New Class of Reciprocal–Orthogonal Parametric Transforms

Content Provider	IEEE Xplore Digital Library
Author	Bouguezel, S. Ahmad, M.O. Swamy, M.N.S.
Copyright Year	2004
Abstract	In this paper, a new class of reciprocal-orthogonal parametric (ROP) transforms having 3N/2 independent parameters for a sequence length N that is a power of two is proposed. The basic idea behind the proposed transforms is to appropriately combine a new parametric kernel with that of the well-known Walsh-Hadamard transform that results in a square parametric matrix operator of order N with some very interesting properties. It is shown that the inverse matrix operator of the proposed class of transforms can be easily obtained by taking the reciprocal of each of the entries of the forward matrix and then transposing the resulting matrix. In addition, a simple method is introduced in order to facilitate the generation of the matrix operator of the proposed ROP transforms. This method is then used specifically to construct new classes of unitary and multiplication-free transforms. Many other new transforms, as well some of the existing ones, can be derived from these proposed ROP transforms. An efficient algorithm is developed for a fast computation of the proposed transforms. In view of the availability of this fast algorithm and the property of easily computable inverse transform, the proposed ROP transforms can be used in many transform-based applications, with their independent parameters providing more degrees of freedom such as affording an additional secret key in watermarking and encryption applications.
Sponsorship	IEEE Circuits and Systems Society
Starting Page	795
Ending Page	805
Page Count	11
File Size	555396
File Format	PDF
ISSN	15498328
Volume Number	56
Issue Number	4
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-04-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Discrete transforms Watermarking Cryptography Signal processing algorithms Discrete Fourier transforms Discrete cosine transforms Error correction codes Quantum computing Fourier transforms Signal processing Walsh–Hadamard transform (WHT) Complex Hadamard matrices reciprocal–orthogonal parametric (ROP) transforms and matrices unitary transforms
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering Hardware and Architecture

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