Computing running DCTs and DSTs based on their second-order shift properties

This paper presents a set of second-order recursive equations which are referred to as the second-order shift (SOS) properties of the discrete cosine transform (DCT) and the discrete sine transform (DST). The proposed SOS properties enable independent updating of the respective DCT and DST coefficients. This is in direct contrast with existing methodology for computing the running DCT and DST where there is an inherent interdependency between the DCT and DST coefficients. The SOS properties provide more efficient algorithms in terms of computational burden and memory requirements when implementing running DCTs and DSTs.