New fast Walsh–Hadamard–Hartley transform algorithm

Suha Suliman Mardan, Mounir Taha Hamood


This paper presents an efficient fast Walsh–Hadamard–Hartley transform (FWHT) algorithm that incorporates the computation of the Walsh-Hadamard transform (WHT) with the discrete Hartley transform (DHT) into an orthogonal, unitary single fast transform possesses the block diagonal structure. The proposed algorithm is implemented in an integrated butterfly structure utilizing the sparse matrices factorization approach and the Kronecker (tensor) product technique, which proved a valuable and fast tool for developing and analyzing the proposed algorithm. The proposed approach was distinguished by ease of implementation and reduced computational complexity compared to previous algorithms, which were based on the concatenation of WHT and FHT by saving up to 3N-4 of real multiplication and 7.5N-10 of real addition.


discrete Hartley transform; Fast algorithms; kronecker product; orthogonal transforms; Walsh–Hadamard transform;

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International Journal of Electrical and Computer Engineering (IJECE)
p-ISSN 2088-8708, e-ISSN 2722-2578