Title: Complex Hadamard transform of digital signals: properties and applications

Authors: Rumen P. Mironov; Roumen K. Kountchev

Addresses: Department of Radio Communications and Video Technologies, Faculty of Telecommunications, Technical University of Sofia, Sofia, Bulgaria. ' Department of Radio Communications and Video Technologies, Faculty of Telecommunications, Technical University of Sofia, Sofia, Bulgaria

Abstract: In this paper, we present a class of Complex Hadamard matrices, which are constructed on the base of well-known real Hadamard construction algorithm. The general properties of the developed matrices are discussed and algorithms for reordering and fast calculation of spectral coefficients are given. On the basis of theoretical investigations two applications of complex Hadamard transformation in the area of multidimensional digital signal processing are given. A new method for audio watermarking in the phase spectrum of audio signals and new method for spectrum optimisation of truncated orthogonal transforms are presented. The obtained result lead to the conclusion, that the elaborated complex Hadamard transform can be used efficiently in digital signal processing for spectral analysis, pattern recognition, digital watermarking, transformation, coding and transmission of one-dimensional and two-dimensional signals.

Keywords: digital signal processing; DSP; complex Hadamard transform; data compression; fast unitary transforms; image processing; optimal truncated transforms; audio watermarking; spectrum optimisation; truncated orthogonal transforms; pattern recognition.

DOI: 10.1504/IJRIS.2012.046487

International Journal of Reasoning-based Intelligent Systems, 2012 Vol.4 No.1/2, pp.3 - 16

Available online: 09 Apr 2012 *

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