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The discrete Hartley transforms (DHT) of types I -IV and the related matrix algebras are discussed. We prove that any of these DHTs of length N = 2 t can be factorized by means of a divide-and-conquer strategy into a product of sparse, orthogonal matrices where in this context sparse means at most two nonzero entries per row and column. The sparsity joint with orthogonality of the matrix factors is the key for proving that these new algorithms have low arithmetic costs equal to 5 2 N log 2 (Ndoi:10.4310/cis.2005.v5.n1.a2 fatcat:emdsaav7vjawznlnq7gfdh5ziy