Fast Algorithms for the Discrete Cosine Transform

We introduce several fast algorithms for computing discrete cosine transforms (DCT’s) and their inverses on multidimensional inputs of sizes which are powers of 2. Because the one-dimensional 8-point DCT and the two-dimensional 8 x 8-point DCT are so widely used, we discuss them in detail. We also present algorithms for computing scaled DCT’s and their inverses; these have applications in compression of continuous tone image data, where the DCT is generally followed by scaling and quantization. © 1992 IEEE