Direct N-point DCT computation from three adjacent N/3-point DCT coefficients

An efficient method for computing a length-N DCT given three consecutive length-N/3 DCTs is proposed. This method differs from previous ones in that it reduces considerable arithmetic operations and uses only length-N/3 DCTs instead of length-N DCTs. We also find its great applications in fractional scaling of a DCT-based image by the factor of N/2^α3^β. This would be very useful in HDTV standard, whose display size is usually 16:9. The comparison with conventional methods is provided in this paper.