Matrix Expansions for Computing the Discrete Hartley Transform for blocklength N0 (mod 4)

Abstract — A new fast algorithm for computing the discrete Hartley transform (DHT) is presented, which is based on the expansion of the transform matrix. The algorithm presents a better performance, in terms of multiplicative complexity, than previously known fast Hartley transform algorithms and same performance, in terms of additive complexity, than Split-Radix algorithm. A detailed description of the computation of DHTs with blocklengths 8 and 16 is shown. The algorithm is very attractive for blocklengths N ≥ 128