A binary friendly algorithm for computing discrete Hartley transform

Abstract

The discrete Hartley transform (DHT) has found use in signal processing. A binary friendly algorithm for computing the DHT is proposed. This is possible, if the transform size N is a Ramanujan number. The use of Ramanujan numbers has been proposed by Bhatnagar (see Signal Processing, vol.43, p.93-101, 1996) for the computation of the discrete Fourier transform (DFT) via shift and addition operations. Direct computation of the DHT of size N, requires O(N/sup 2/) arithmetical operations. However, if N is permitted to be a Ramanujan number, then the DHT can be computed sequentially with a single adder in O(N/sup 2/) addition times, plus the time required for the normalizing (division) operations. The use of these numbers permits the computation of DHT in O(N/sup 2/) shift and addition operations, and O(N) division operations. A parallel implementation of the algorithm can be executed in O(N) addition times, with O(N) number of adders, in addition to the time required for the normalization operations.