Combined Polynomial Transform and Radix-q Algorithm for Multi-dimensional DCT-III

Authors:
Yonghong Zeng;Guoan Bi;Zhiping Lin
Affiliations:
Research fellow in the School of EEE, Nanyang Technological University, Singapore. Associate professor in the National University of Defense Technology, P.R. Chinaeyhzeng@ntu.edu.sgegbi@ntu.edu.sg;Associate professor in the School of EEE, Nanyang Technological University, Singaporeezplin@ntu.edu.sg
Venue:
Multidimensional Systems and Signal Processing
Year:
2002

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Abstract

By combining the polynomial transform and radix-q decomposition, the paper presents a new algorithm for the type-III r-dimensional discrete Cosine transform (rD-DCT-III) with size ql1×ql2×…×qlr, where q is an odd prime number. The number of multiplications for computing an rD-DCT-III is approximately 1/r times that needed by the row-column method while the number of additions increase slightly. The total number of operations (additions plus multiplications) is also reduced. The proposed algorithm has a simple computational structure because it needs only 1D-DCT-III and the polynomial transform.