Multiplication-free 8×8 2D DCT architecture using algebraic integer encoding

A novel architecture for a 2D 8×8 discrete cosine transform (DCT) is presented. The architecture uses a new algebraic integer encoding of a one dimensional radix-8 DCT that allows the separable computation of a 2D 8×8 DCT without any intermediate number representation conversions. This is a considerable improvement on previously introduced algebraic integer encoding techniques. Using this encoding scheme, an entire 8×8 2D DCT-SQ (scalar quantisation) algorithm can be implemented with only 24 adders.