Odd type DCT/DST for video coding: Relationships and low-complexity implementations

In this paper, we show a class of relationships which link Discrete Cosine Transforms (DCT) and Discrete Sine Transforms (DST) of types V, VI, VII and VIII, which have been recently considered for inclusion in the future video coding technology. In particular, the proposed relationships allow to compute the DCT-V and the DCT-VIII as functions of the DCT-VI and the DST-VII respectively, plus simple reordering and sign-inversion. Moreover, this paper exploits the proposed relationships and the Winograd factorization of the Discrete Fourier Transform to construct low-complexity factorizations for computing the DCT-V and the DCT-VIII of length 4 and 8. Finally, the proposed signal-flow-graphs have been implemented using an FPGA technology, thus showing reduced hardware utilization with respect to the direct implementation of the matrix-vector multiplication algorithm.