Multidimensional fourier transforms by systolic architectures

In this paper, time-efficient systolic and semi-systolic architectures for the implementation of multidimensional DFTs are proposed that allow modularity and easy expansibility while keeping throughput independent of the dimension of the DFT. We shall call an array semi-systolic if the input data is to be preloaded into every cell of the array or if the output data can be calculated not only in the boundary cells of the array. DFT algorithms are represented by FORTRAN-like code, in order to explicitly display the suggested rotational transformations in the index space. After the transformation, multidimensional DFT algorithm can be mapped onto a systolic structure. The area-time2 complexity of the proposed design is within logk factor of the lower bound for ak-point DFT (AT2=Ω(k2 log2k)), i.e. equals 0(k2 log3k)=0(N2M log3N) fork=N2M point DFT;A is the area complexity andT is the system throughput.

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