Unified Parallel Lattice Structures for Time-Recursive Discrete Cosine/Sine/Hartley Transforms

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The problems of unified efficient computations of the discrete cosine transform (DCT), discrete sine transform (DST), discrete Hartley transform (DHT), and their inverse transforms are considered. In particular, a new scheme employing the time- recursive approach to compute these transforms is presented. Using such approach, unified parallel lattice structures that can dually generate the DCT and DST simultaneously as well as the DHT are developed. These structures can obtain the transformed data for sequential input time recursively and the total number of multipliers required is a linear function of the transform size N. Furthermore, there is no any constraint on N. The resulting architectures are regular, module, and without global communication so that it is very suitable for VLSI implementation for high-speed applications such as ISDN network and HDTV system. It is also shown in this paper that the DCT, DST, DHT and their inverse transforms share an almost identical lattice structure. The lattice structures can also be formulated into pre-lattice and post-lattice realizations. Two methods, the SISO and double- lattice approaches, are developed to reduce the number of multipliers in the parallel lattice structure by 2N and N respectively. The trade-off between time and area for the block data processing is also considered.