New 2ⁿ discrete cosine transform algorithm using recursive filter structure

Abstract

It is always desirable to look for more efficient algorithms for the realization of the discrete cosine transform (DCT). In this paper, we generalize a formulation for converting a length-2ⁿ DCT into n groups of equations, then apply a novel technique for its implementation. The sizes of the groups are 2[sup m], for m = n-1, ...., 0. While their structures are extremely regular. The realization can then be converted into the simplest recursive filter form, which is of particularly simple for practical implementation.