Implementation of real-valued discrete transforms via encoding algebraic integers

In this paper, we propose a novel approach for computing real-valued discrete transforms such as the discrete cosine transform and the discrete Hartley transform. The approach is based on the algebraic integer encoding scheme. With the aid of this scheme, an error-free representation of the cos, sin and cas functions becomes possible. Furthermore, for the implementation of these algorithms a fully pipelined systolic architecture with O(N) throughput is proposed.