Conjugate Symmetric Sequency-Ordered Complex Hadamard Transform

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 disc...

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Veröffentlicht in:	IEEE transactions on signal processing 2009-07, Vol.57 (7), p.2582-2593
Hauptverfasser:	Aye Aung, Boon Poh Ng, Rahardja, S.
Format:	Artikel
Sprache:	eng
Schlagworte:	Algorithms Applied sciences Coding, codes Complex Hadamard transforms Computational modeling Computer simulation conjugate symmetric sequency-ordered complex Hadamard transform (CS-SCHT) Conjugates Detection, estimation, filtering, equalization, prediction Discrete Fourier transforms discrete orthogonal transforms Discrete transforms dyadic shift invariant Exact sciences and technology Factorization fast algorithms Fourier transforms Frequency Image coding Image compression Information, signal and communications theory Invariants Logic design Miscellaneous Signal and communications theory Signal processing Signal representation. Spectral analysis Signal, noise Sparse matrices Spectral analysis Symmetric matrices Telecommunications and information theory Transforms
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Zusammenfassung:	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.
ISSN:	1053-587X 1941-0476
DOI:	10.1109/TSP.2009.2017572