Multiplierless Recursive Algorithm Using Ramanujan Ordered Numbers

Abstract

A special class of recursive multiplierless transforms for computing Discrete Cosine Transform (DCT) is introduced. DCT computation requires evaluation of cosine angles which are multiples of 2π/N. The proposed algorithm uses Ramanujan ordered number of degree-2 which is represented as 2⁻¹ + 2^−m. Thus the cosine functions can be computed by shifts and adds, employing Chebyshev type of recursion. With this algorithm, the floating-point multiplication is completely eliminated, and hence, the multiplierless algorithm can be implemented using shifts and additions only. The orthogonality of the recursive DCT kernel is well maintained through matrix factorization to reduce the computational complexity. The inherent parallel structure yields simpler programming and hardware implementation and provides additions and shifts which is very much less complex when compared to other recent multiplierless algorithms.

Keywords:

• Fast discrete cosine transform
• Multilplerless
• Ramanujan ordered number
• Recursive

Additional information

Notes on contributors

K. S. Geetha

K. S. Geetha received her B.E and M.Tech in Electronics Engineering from National Institute of Engineering, Mysore, India, in 1991 and 1998. She is currently an Assistant Professor with the Department of Electronics and Communication Engineering, R.V. College of Engineering, Bangalore, India currently working towards her PhD degree. Her research interests include digital signal processing, image and video processing. E-mail: [email protected]

M. Uttarakumari

M. Uttarakumari received her B.E from Nagarjuna University in 1989 and M.Tech from Bangalore University in 1996 and Ph.D degree from Andhra university in 2007. She is currently Professor with the Department of Electronics and Communication Engineering, R.V. College of Engineering, Bangalore, India. Her current research interests include image compression, watermarking, digital signal processing. E-mail: [email protected]