Fast Radix-3 Algorithm for the Generalized Discrete Hartley Transform of Type II
We present a new fast radix-3 algorithm for the computation of the length-<i>N</i> generalized discrete Hartley transform of type-II (GDHT-II), where <i>N</i> = 3<sup>m</sup>, <i>m</i> ≥ 2. Then we apply this algorithm to the direct computation of length-<i>N</i> GDHT-II coefficients when given three adjacent length-<i>N</i>/3 GDHT-II coefficients. The computational complexity of the proposed method is lower than that of the traditional approach for length <i>N</i> ≥ 9. The arithmetic operations can be saved from 19% to 29% for <i>N</i> = 3<sup>m</sup> varying from 9 to 243 and from 17% to 29% for <i>N</i> = 3×2<sup>m</sup> varying from 12 to 384. Furthermore, the new approach can be easily implemented.