New algorithm for r-dimensional DCT-II

The paper shows that the type-II r-dimensional discrete cosine transform (r D-DCT-II) of size q(l1) x q(l2) x...x q(lr), where r > 1 and q is an odd pr ime number, call be converted into a series of one-dimensional reduced DCT- IIs by using the polynomial transform. The number of multiplications for co mputing an rD-DCT-II is significantly reduced compared to that needed by th e row-column method. The total number of arithmetic operations (additions p lus multiplications) needed by the proposed algorithm is also reduced subst antially. In addition to the capability of dealing with different dimension al sizes, the proposed algorithm also has a simple computational structure because it requires only the 1D-DCT-II and the polynomial transform.