A progressive, recursive, fast, discrete cosine transform

A new algorithm to calculate the discrete cosine transform (DCT) and its inverse is described. The algorithm is recursive in that it breaks the DCT transformation of an array of size N into two DCTs of size N/2. The proposed recursive algorithm has the ability to gradually reconstruct the original data from its DCT array, with progressively higher levels of resolution. In regard to speed, it requires O(N logN) operations, where N is the array size, but it is not the fastest algorithm if only the full resolution reconstruction is desired. The algorithm can be extended to multidimensional arrays in a straightforward way