Fast algorithms for generalized discrete Hartley transform

Based on the prime factor decomposition, this paper presents fast algorithms for type-III generalized discrete Hartley transform (GDHT). When N = p*q, where p and q are mutually prime, the length-N GDHT can be decomposed into p length-q type-III GDHT and q length-p type-III discrete cosine transform (DCT). The proposed algorithms achieve a substantial reduction of the number of additions and multiplications and possess a regular computational structure. In particular, a simple index mapping method is proposed to minimize the overall implementation complexity and cost.