Fast regular 2-D algorithms for trigonometric transforms

Two-dimensional fast cosine and sine transforms with regular structure are developed for 2(n) x 2(n) data points. These algorithms are extended versions of the 1-D fast regular algorithms introduced in our recent paper(1). The rationale for these 2-D algorithms for sine/cosine transforms is a 2-D decomposition of data sequences into 2-D subblocks with reduced dimension, rather than one-dimensional, separable treatments for the columns and rows of the data sets. As a result the number of multiplications is 25% less than in row-column approach. Numerous algorithms of these type were proposed previously for Discrete Fourier Transform (DFT) and Discrete Cosine Transform of type 2 (DCT-II). In DCT-II case the algorithms do not have a regular structure as is the case in DFT algorithms and motivation of this work is to derive 2-D algorithms for discrete sine and cosine transforms (DCT-II, DCT-III, DCT-IV, DST-II, DST-III, DST-TV) with regular constant geometry structures. Extension to 2(n) x 2(m) data points is straightforward.