Practical fast 1-D DCT algorithms with 11 multiplications

A class of practical fast algorithms is introduced for the discrete cosine transform (DCT). For an 8-point DCT only 11 multiplications and 29 additions are required. A systematic approach is presented for generating the different members in this class, all having the same minimum arithmetic complexity. The structure of many of the published algorithms can be found in members of this class. An extension of the algorithm to longer transformations is presented. The resulting 16-point DCT requires only 31 multiplications and 81 additions, which is, to the authors' knowledge, less than required by previously published algorithms.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>