Multidimensional algebraic-integer encoding for high performance implementation of DCT and IDCT

A recently introduced single variable algebraic integer encoding scheme allows low complexity error-free computation of the DCT and IDCT. Introduced is the use of multidimensional algebraic-integer encoding of the transformation matrix of the DCT and IDCT which increases the sparseness of the encoding matrix and substantially reduces the dynamic range of the transformation coefficients. The computational savings are approximately 20% for typical image compression applications.