Unified parallel lattice structures for time-recursive discrete cosine/sine/Hartley transforms

Unified efficient computations of the discrete cosine transform (DCT), discrete sine transform (DST), discrete Hartley transform (DHT), and their inverse transforms employing the time-recursive approach are considered. Unified parallel lattice structures that can dually generate the DCT and DST simultaneously as well the DHT are developed. These structures can obtain the transformed data for sequential input time recursively with a throughput rate of one per clock cycle. The total number of multipliers required is a linear function of the transform size N, with no constraint on N. The resulting architectures are regular, modular, and without global communication so that they are very suitable for VLSI implementation for high-speed applications. It is shown that the DCT, DST, DHT and their inverse transforms share an almost identical lattice structure. The tradeoff between time and area for the block data processing is considered