Conjugate symmetric sequency-ordered complex Hadamard transform

Authors:
Aye Aung;Boon Poh Ng;Susanto Rahardja
Affiliations:
School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore;School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore;Institute for Infocomm Research, Agency for Science, Technology, and Research, Singapore
Venue:
IEEE Transactions on Signal Processing
Year:
2009

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Abstract

A new transform known as conjugate symmetric sequency-ordered complex Hadamard transform (CS-SCHT) is presented in this paper. The transform matrix of this transform possesses sequency ordering and the spectrum obtained by the CS-SCHT is conjugate symmetric. Some of its important properties are discussed and analyzed. Sequency defined in the CS-SCHT is interpreted as compared to frequency in the discrete Fourier transform. The exponential form of the CS-SCHT is derived, and the proof of the dyadic shift invariant property of the CS-SCHT is also given. The fast and efficient algorithm to compute the CS-SCHT is developed using the sparse matrix factorization method and its computational load is examined as compared to that of the SCHT. The applications of the CS-SCHT in spectrum estimation and image compression are discussed. The simulation results reveal that the CS-SCHT is promising to be employed in such applications.