A new fast algorithm for computing prime-Length DCT through cyclic convolutions

摘要

This paper proposes a new algorithm for the computation of discrete cosine transform (DCT) with an odd prime length using cyclic or skew cyclic convolutions. The algorithm separates DCT coefficients into three parts: DC, even-indexed and odd-indexed DCT coefficients. Making use of the number theory, a new index-mapping operation is defined. By means of the index-mapping operation, the even-indexed part is converted to a cyclic convolution, and the odd-indexed part is converted to a cyclic or skew cyclic convolution depending upon its length. Some efficient and fast cyclic convolution algorithms can now be applied to this approach. The resultant formulation has low computational complexity, simple and regular structure as compared to the related approaches in the literature.