Recursive algorithms for discrete cosine transform

The discrete cosine transform (DCT) is one of the most widely used transforms in digital signal processing. A recursive algorithm with a regular structure is first presented for computing the discrete cosine transform (DCT-II), it requires no data shifts, the multiplication coefficients can be generated by a simple recursion. Then the recursive algorithms for DCT-I and DCT-IV are presented. These algorithms have a better stability, with a complexity which is the same as that of Lee (1984) and Wang (1985), making them very useful in practice.