New algorithms for multidimensional discrete Hartley transform (Q1603609)

New fast algorithms for multidimensional discrete Hartley transform (MD-DHT) are presented. Based on the index mapping and multidimensional polynomial transform (PT), the MD-DHT is converted into a series of one-dimensional type-II discrete W transform and PTs. The proposed fast algorithms achieve considerable savings on the number of operations. For example, the number of multiplications for computing an \(r\)-dimensional DHT is only \(1/r\) times that needed by the row-column method, and the number of additions is also reduced considerably. Detailed analysis of the computational complexity is also presented.