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