Optimal Architectures for Multidimensional Transforms.
JaJa, Joseph F.
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Multidimensional transforms have widespread applications in computer vision, pattern analysis and image processing. The only existing optimal architecture for computing multidimensional DFT on data of size n = Nd requires very large rotator units of area O(n^2) and pipeline-time O(log n). In this paper we propose a family of optimal architectures with areatime trade-offs for computing multidimensional transforms. The large rotator unit is replaced by a combination of a small rotator unit, a transpose unit and a block rotator unit. The combination has an area of O(N^(d+2a)) and a pipeline time of O(N^(d/2-a)log n), for 0 < a < d/2. We apply this scheme to design optimal architectures for two-dimensional DFT, DHT and DCT. The computation is made efficient by mapping each of the one-dimensional transforms involved into two dimensions.