| ARTICLE |
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| Year : 2010 | Volume
: 56
| Issue : 4 | Page : 182-188 |
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Multiplierless Recursive Algorithm Using Ramanujan Ordered Numbers
KS Geetha, M Uttarakumari
Department of ECE, R.V.College of Engineering, Bangalore, India
Correspondence Address:
K S Geetha
Department of ECE, R.V.College of Engineering, Bangalore
India
 DOI: 10.4103/0377-2063.70615
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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-l+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 3/2Nlog2N-N+1 additions and N/2log2N shifts which is very much less complex when compared to other recent multiplierless algorithms. |
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