A Novel Cosine Approximation for High-Speed Evaluation of DCT

This article presents a novel cosine approximation for high-speed evaluation ofDCT (Discrete Cosine Transform) using Ramanujan Ordered Numbers. Theproposed method uses the Ramanujan ordered number to convert the angles ofthe cosine function to integers. Evaluation of these angles is by using a 4thdegree polynomial that approximates the cosine function with error ofapproximation in the order of 10-3. The evaluation of the cosine function isexplained through the computation of the DCT coefficients. High-speedevaluation at the algorithmic level is measured in terms of the computationalcomplexity of the algorithm. The proposed algorithm of cosine approximationincreases the overhead on the number of adders by 13.6%. This algorithmavoids floating-point multipliers and requires N/2log2N shifts and (3N/2 log2 N)- N+ 1 addition operations to evaluate an N-point DCT coefficients therebyimproving the speed of computation of the coefficients