Efficient implementation of discrete cosine transform using recursive filter structure

We generalize a formulation for converting a length-2ⁿ discrete cosine transform into n groups of equations, then apply a novel technique for its implementation. The sizes of the groups are 2^n-1 , 2^n-2, ...2⁰ respectively, while their structures are extremely regular. The realization can then be converted into recursive filter form, which is particularly simple for practical implementation