A new hardware-efficient algorithm and architecture for computation of 2-D DCTs on a linear array

A new recursive algorithm with hardware complexity of O(log₂ N) is derived for fast computation of N×N 2-D discrete cosine transforms (2-D DCTs). It first converts the original 2-D data matrices into 1-D vectors and then employs different partition methods for the input and output indices in the 1-D vector space. Afterward, the algorithm computes the corresponding 2-D complex DCT (2-D CCT) and then uses a post-addition step to produce simultaneously two 2-D DCT outputs. The decomposed form of the 2-D recursive algorithm looks like a radix-4 fast Fourier transform algorithm. The common entries in each row of the butterfly-like matrix are factored out in order to reduce the number of multipliers needed during implementation. A new linear architecture for the derived algorithm is presented which leads to a hardware-efficient architectural design requiring only log₂N complex multipliers plus 3log₂N complex adders/subtractors for the computation of a 2-D N×N CCT