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.