Triple-Matrix Product-Based 2D Systolic Implementation of Discrete Fourier Transform

Publication Type:

Journal Article


Circuits, Systems, and Signal Processing, Springer US, Volume 34, Issue 10, p.3221-3239 (2015)




Dept. of Electronics and communication Engineering.


Realization of NN -point discrete Fourier transform (DFT) using one-dimensional or two-dimensional systolic array structures has been developed for power of two DFT sizes. DFT algorithm, which can be represented as a triple-matrix product, can be realized by decomposing NN into smaller lengths. Triple-matrix product form of representation enables to map the NN -point DFT on a 2D systolic array. In this work, an algorithm is developed and is mapped to a two-dimensional systolic structure where DFT size can be non-power of two. The proposed work gives flexibility to choose NN for an application where NN is a composite number. The total time required to compute NN -point DFT is 2(N1−1)+N2+N2(N1−1)+N2+N for any N=N1N2N=N1N2 . The array can be used for matrix–matrix multiplication and also to compute the diagonal elements of triple-matrix multiplication for other applications. The proposed architecture produces in-order stream of DFT sequence at the output avoiding need for reordering buffer. Large sized DFT can be computed by repeatedly using the proposed systolic array architecture.