Fast algorithms for generalized discrete Hartley transform of composite sequence lengths

This paper presents fast algorithms for type-II, type-III, and type-IV generalized discrete Hartley transform. In particular, new odd-factor algorithms are derived to support transforms whose sequence length contains multiple odd factors. By jointly using the odd-factor and radix-2 algorithms, fast computation for arbitrarily composite sequence length can be achieved. Compared to other reported algorithms, the proposed ones have a regular computational structure, achieve a substantial reduction of computational complexity, and support a wider range of choices on the sequence length.