Fast computing of discrete cosine and sine transforms of types VI and VII

We propose fast algorithms for computing Discrete Sine and Discrete Cosine Transforms (DCT and DST) of types VI and VII. Particular attention is paid to derivation of fast algorithms for computing DST-VII of lengths 4 and 8, which are currently under consideration for inclusion in ISO/IEC/ITU-T High Efficiency Video Coding (HEVC) standard.