Systolic architecture implementation of 1D DFT and 1D DCT

Discrete Fourier Transform is widely used in signal processing for spectral analysis, filtering, image enhancement, OFDM etc. Cyclic convolution based approach is one of the techniques used for computing DFT. Using this approach an N point DFT can be computed using four pairs of [(M-1)/2]-point cyclic convolution where M is an odd number and N=4M. This work proposes an architecture for convolution based DFT and its FPGA implementation. Proposed architecture comprises of a pre-processing element, systolic array and a post processing stage. Processing element of systolic array uses a tag bit to decide on the type of operation (addition/subtraction) on the input signals. Proposed architecture is simulated for 28 point DFT using ModelSim 6.5 and synthesized using Xilinx ISE10.1 using Vertex 5 xc5vfx100t-3ff1738 FPGA as the target device and can operate at a maximum frequency of 224.9MHz. The performance analysis is carried out in terms of hardware utilization and computation time and compared with existing similar architectures. Further, as the convolution based DCT has two systolic arrays similar to that of DFT, a unified architecture is proposed for 1D DFT/1D DCT.