This project developed efficient, self-recursive, and fast split-radix and radix-4 algorithms for the Discrete Cosine Transforms (DCT) based on different boundary conditions. The project also addresses the self-recursive and stable aspects of split-radix and radix-4 DCT algorithms having simple, sparse, and scaled orthogonal factors. Moreover, the developed split-radix and radix-4 algorithms attain the lowest theoretical multiplication complexity and flop counts for 8-point DCT matrices in the literature. Numerical results are presented for the arithmetic complexity comparison of the proposed algorithms with the known fast and stable DCT algorithms. Software implementations have been written based on the proposed DCT algorithms. These results show that the proposed algorithms have attained low arithmetic complexity. The execution time of the proposed algorithms is presented while verifying the connection to the order of the flop counts. It is shown that the execution time of the proposed split-radix and radix-4 algorithms are more efficient than the existing radix-2 DCT algorithms. Finally, spectral analysis has been conducted based on the proposed DCT algorithms
