THE EFFICIENT MEMORY-BASED VLSI ARRAY DESIGNS FOR DFT AND DCT

In this paper, the efficient memory-based VLSI arrays and the accompanied new design approach for the discrete Fourier transform (DFT) and discrete cosine transform (DCT) are presented. The DFT and DCT are formulated as cyclic convolution forms and mapped into linear arrays which characterize small numbers of I/O channels and low I/O bandwidth. Since the multipliers consume much hardware area, the presented designs utilize small ROM's and adders to implement the multiplications, which is based on good data arrangements exploiting the number properties of the transform kernels. Moreover, the ROM size can be reduced effectively by arranging the data in our designs appropriately. Typically, to perform 1-D N-point DFT and DCT, the arrays need N X 2L words of ROM only. Compared to the conventional distributed arithmetic architectures which should require N X 2N words of ROM, much memory can be saved if N is greater than L, which occurs in most DFT applications. To summarize, the presented arrays outperform others in the architectural topology (local and regular connection), computing speeds, hardware complexity, the number of I/O channels, and I/O bandwidth. They take the advantages of both systolic arrays and the memory-based architectures.