Fast Radix-319 Discrete Hartley Transform

An efficient radix-319 fast Hartley transform (FHART) al- gorithm is proposed. It shows a great improvement over the previous radix-3 FHART algorithm such that nearly 50% of the number of mul- tiplications is saved. For the computation of real-valued discrete Fou- rier transforms (DFT's) with sequence lengths which are powers of 3, the proposed radix-3/9 algorithm also gives a significant improvement over the fastest real-valued radix-3/9 fast Fourier transform (FFT) al- gorithm.