Complex Hadamard transform of digital signals: properties and applications

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.

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