On Prime Factor Mapping for the Discrete Hartley Transform Daniel P.-K. Lun, Student Member, IEEE, and Wan-Chi Siu, Senior Member, ZEEE
Kong Polytechnic · 1992
When compared with the complexity for realizing the prime factor DFT, the prime factor discrete Hartley trans- form requires some extra arithmetic operations for the real- ization of the prime factor mapping. These extra arithmetic op- erations can take up as much as 40% of the total arithmetic operations required. In this paper, we propose a new prime factor mapping scheme, which requires no extra arithmetic op- erations, for the computation of the discrete Hartley trans- form. It is achieved by embedding all the extra arithmetic op- erations into the subsequent short length computations, whereas the computational complexities of these embedded short lengths remain unchanged. Consequently, the present approach signif- icantly eliminates the burden which is introduced by the extra arithmetic operations. With our new prime factor mapping scheme, we further demonstrate that a prime-factor-mapped DHT would have a superb performance as compared with other fast discrete Hartley transform algorithms.