A two-dimensional fast cosine transform

A two-dimensional fast cosine transform algorithm (2-D FCT) is developed for 2^m× 2ⁿdata points. This algorithm is an extended version of the 1-D FCT algorithm introduced in a recent paper, but with significantly reduced computations for a 2-D field. The rationale for this 2-D FCT is a 2-D decomposition of data sequences into 2- D subblocks with reduced dimension (halves), rather than serial, one-dimensional, separable treatment for the columns and rows of the data sets. Computer simulation for the 2-D FCT algorithms, using a smaller block of data and finite word precision, proves to be excellent in comparison with the direct 2-D discrete cosine transform (2-D DCT). An example of a 4 × 4 2-D inverse fast cosine transform (2-D IFCT) algorithm development is presented in this paper, together with a signal flow graph.