Practical fast 1-D DCT Algorithms with 11 Multiplications.

A new class of practical fast algorithm is introduced for the Discrete Cosine Transform (DCT), an important transform that is of particular interest in image compression. For an 8- point DCT only 11 multiplications and 29 additions are required. A systematic approach is presented to generate 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 for longer transformations is presented. As a result, the 16-point DCT requires only 31 multiplications and 81 additions, which is, to our knowledge, less than the currently published algorithms.