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A new multiplierless discrete cosine transform based on the Ramanujan ordered numbers for image coding

The performance of image coding can be improved upon by using a special class of multiplierless discrete cosine transform using Ramanujan numbers termed as Ramanujan DCT (RDCT). Ramanujan ordered numbers are those which approximate 2π/N by 2 2 l m − − + , where l and m are integers. The cosine angles can then be computed using Chebyshev type of recursion using only shifters and adders. Fast forward and backward transformation may be achieved. Analysis and simulations show that the proposed RDCT maintains good de-correlation and energy compaction properties of the DCT and the error due to approximation is almost zero at lower spectral components and relatively low at higher spectral components. Simulation experiments are provided to justify that the proposed algorithm is best suited for image compression.