A two-dimensional fast cosine transform algorithm based on Hou's approach

Abstract

A structured approach is used to generate a fast algorithm to compute two-dimensional discrete cosine transforms (DCT) based on Hou's method. Hou's algorithm is extended to the 2-D case using an approach presented in both matrix and diagrammatical forms. The matrix approach is discussed, and this forms a basis on which a 2-D fast DCT algorithm is derived. It is shown that this matrix method has a structure similar to that of the 1-D Cooley-Tukey fast Fourier transform (FFT) algorithm. Then the decimation-in-frequency (DIF) 2-D fast DCT algorithm is presented using matrix forms which use the tensor (or Kronecker) product as a construction tool. Finally, the 2-D algorithm is described by logic diagrams which reveal the relationship between the 2-D algorithm and its 1-D counterpart. As an example, the logic diagram of an 8-point*8-point 2-D DCT using the new 2-D DCT algorithm is generated through a simple procedure.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>