New 2n discrete cosine transform algorithm using recursive filter structure

The discrete cosine transform (DCT) is widely used in digital signal processing. It is always desirable to look for more efficient algorithms for the realization of the DCT. We generalize a formulation for converting a length-2ⁿ DCT into n groups of equations, then apply a novel technique for its implementation. The sizes of the groups are 2^m, for m=n-1,...,0. While their structures are extremely regular. The realization can then be converted into the simplest recursive filter form, which is of particularly simple for practical implementation. The filter structure is numerically stable, since it involves no division at all