Effects of finite register length in the fast hartley transform
Ken’ichi Furuya, Hikaru Date, Kimitoshi Fukudome · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1992
Abstract This paper discusses the effect of finite register length on the computation accuracy of the fast Hartley transform (FHT) and derives a theoretical statistical expression for the mean‐square computation error. Theoretical proofs are presented which show that: (i) the computation error of a fixed‐point FHT is proportional to the square of the number of data (N); (ii) the computational error is proportional to N if scaling is used to prevent an overflow in the fixed‐point FHT; (iii) the computational error is proportional to log N in the case of the floating‐point FHT; and (iv) the computation error is halved by increasing the register length by 1 bit. An experiment was conducted to verify those properties.