Abstract—This paper proposes a new multidimensional (m-D) multiplierless Ramanujan Numbered Discrete Cosine Transform (RDCT) based coding to improvise the coding efficiency in the visual data compression for multimedia applications. In this paper, the mD-DCT with size N1N2Nm , where i N power of 2 is, can be converted into a series of one dimensional (1-D) DCT’s which are evaluated using Ramanujan Ordered Numbers thereby making the algorithm multiplierless. The proposed algorithm achieves considerable savings in terms of shift operations compared with the row-column approach thus making it suitable for image and video coding applications. For a 3-dimensional input data of size 888, the algorithm reduces the number of shift operations by 66% compared to multidimensional row-column approach and approximately 0.1% increase in the number of adders compared with the row-column approach. Compared with the other recently presented multidimensional DCT algorithms, the proposed one gives better result as it uses the shift operations instead of the floating-point multipliers and also achieves considerable reduction in the number of addition operation .

Index Terms—Discrete cosine transform, fast multiplierless algorithm, Ramanujan ordered number, polynomial transform.

The authors are with Faculty, R. V. College of Engineering, Bangalore, India (e-mail: geethakomandur@gmail.com)

Cite:Geetha. K. S and M. Uttarakumari, "Multidimensional Fast Multiplierless DCT Algorithm Using Ramanujan Ordered Numbers," International Journal of Computer and Electrical Engineering vol.4, no.4, pp. 511-514, 2014.