Fast multiplierless recursive transforms using Ramanujan numbers

A special class of multiplierless transforms for computing discrete cosine transform (DCT) is introduced. This algorithm is completely multiplierless to compute an N-point DCT using Ramanujan Number of order -1 and order-2. The algorithm requires evaluation of Cosine angles which are multiples of 2π/N. If the transform size N is a Ramanujan Number and if 2π/N ≅ 2−a, then the cosine functions can be computed by shifts and adds employing Chebyshev type of recursion. In this paper, an analytical extension of the algorithm is made for 2-D Ramanujan DCT for image coding applications.