Direct split-radix algorithm for fast computation of type-II discrete Hartley transform

Mounir T. Hamood

Abstract


In this paper, a new split-radix algorithm for fast computation of type-II discrete Hartley transform (DHT-II) is presented. The algorithm is developed through the decimation-in-time (DIT) approach, and implemented by splitting a length N of DHT-II into one DHT-II of length N/2 for even-indexed samples and two DHTs-II of length N/4 for odd-indexed samples. The proposed algorithm possesses the desirable properties such as regularity, in-place calculation and it is characterized by simple closed-form expressions leading to considerable reductions in the arithmetic complexity compared to the existing DHT-II algorithms. Additionally, the validity of the proposed algorithm has been confirmed through analysing the arithmetic complexity by calculating the number of real multiplications and additions and comparing it with the radix-2 DHT-II algorithm.

Keywords


decimation-in-time approach; discrete Hartley transform; generalized DHTs (GDHTs); split-radix algorithm; type-II DHT (DHT-II);



DOI: http://dx.doi.org/10.12928/telkomnika.v18i6.16100

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