An algorithm for calculation of the discrete cosine transform by paired transform

A new algorithm for splitting the one-dimensional (1-D) 2^r-point discrete cosine transform (DCT) into a set of short 2^k-point type-IV DCTs [k=1:(r-1)] is introduced. The splitting is performed by means of paired transformation that is defined by the paired representation of signals with respect to the cosine transform. A proposed method of calculating the 2^r-point cosine transform requires 2^r-1r multiplications and 2^r-1(3r-2)+1 additions when r≥2.