Direct Computation Of Higher-Order Dct Coefficients From Lower-Order Dct Coefficients

An efficient algorithm is proposed that computes the coefficients of a higher-order discrete cosine transform (DOT) from the coefficients of a lower-order DCT. The main feature of this algorithm is that it calculates the DCT coefficients of the larger block sizes from the DCT coefficients of smaller block sizes without any need to generate the inverse DCT. It is more efficient than the standard approach, which involves an inverse as well as DCT, if the standard fast-Fourier transform (FFT) procedure is used. However, it is not as efficient as the standard procedure if DCT and IDCT are generated using the newly discovered Winograd Fourier transform algorithm. This paper develops the computational algorithm for the one-dimensional DCT, then extends it to the two-dimensional DCT.