A novel CORDIC-based array architecture for the multidimensional discrete Hartley transform

In this paper, a coordinate rotation digital computer (CORDIC)-based array architecture is presented for computing the multidimensional (M-D) discrete Hartley transform (DHT). Since the kernel of the M-D DHT is inseparable, the M-D DHT problems cannot be computed through the 1-D DHT´s directly. Bracewell et al. have presented an algorithm for the M-D DHT through the 1-D DHT´s. The existing hardware architectures have been designed using this algorithm. However, the postprocessing required in the algorithm leads to high hardware overhead. This paper presents a new algorithm to compute M-D DHT through a special 1-D transform which is derived through considering both the separable computation and the efficient implementation with CORDIC architectures. This algorithm provides a direct way to compute the M-D DHT separably through 1-D transforms with simpler postprocessing than that in Bracewell´s approach. Also, the algorithm exploits the symmetry of the triangular functions to reduce the computational complexity. Using this algorithm, we design an array architecture for the M-D DHT. This architecture features a systolic computing style, PE´s with a CORDIC structure, low I/O cost, and the encapsulated new M-D DHT algorithm