High-Precision and Arbitrary-length Fixed-Point Fast Hartley Transform without Multiplications

Discrete Hartley transform (DHT) is an important tool in digital signal processing. In this paper, based on our previous work of performing DHT via linear sums of discrete moments, we have made development to eliminate multiplications in discrete Hartley transforms by performing appropriate bit operations and shift in binary system, which can be implemented by integer additions of fixed points. An efficient and regular systolic array is designed to implement it, and the complexity analysis is also given. Different to other fast Hartley transforms, our algorithm can deal with arbitrary length signals and get high precision. The approach is also applicable to multi-dimensional DHT and DHT inverses.