Optimal VLSI networks for multidimensional transforms

This paper presents a new class of AT²-optimal networks for computing the multidimensional discrete Fourier transform. Although optimal networks have been proposed previously, the networks proposed in this paper are based on a new methodology for mapping large K-shuffle networks, K⩾2, onto smaller area networks that maintain the optimality of the DFT network. Such networks are used to perform the index-rotation operations needed by the multidimensional computation. The resulting networks have simple regular layouts, and can be easily partitioned among several chips in order to reduce the number of input-output pins per chip