Direct recursive structures for computing radix-r two-dimensional DCT

In this paper, new recursive structures for computing radix-r two-dimensional discrete cosine transform (2-D DCT) are proposed. Based on the same indices of transform bases, the regular pre-add preprocess is established and the recursive structures for 2-D DCT, which can be realized in a second-order infinite-impulse response (IIR) filter, are derived without involving any transposition procedure. For computation of 2-D DCT, the recursive loops of the proposed structures are less than that of one-dimensional DCT recursive structures, which need data transposition to achieve the so-called row-column approach. With advantages of fewer recursive loops and no transposition, the proposed recursive structures achieve more accurate results than the existed methods. The regular and modular properties are suitable for VLSI implementation.