Efficient mapping scheme for the prime factor discrete Hartley transform

Compared to the complexity for realizing the prime factor discrete Fourier transform (DFT), the prime factor discrete Hartley transform requires some extra arithmetic operations for the realization of the prime factor mapping. These extra arithmetic operations can take up as much as 40% of the total arithmetic operations required. A new prime factor mapping scheme which requires no extra arithmetic operations is proposed for the computation of the discrete Hartley transform. It is achieved by embedding all the extra arithmetic operations into the subsequent short length computations, whereas the arithmetic complexities of these embedded short length modules remain unchanged