Fast algorithms for the discrete cosine transform. (English) Zbl 0762.65103

Feig, Ephraim; Winograd, Shmuel

IEEE Trans. Signal Process. 40, No. 9, 2174-2193 (1992).

Authors’ summary: 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 \(8\times 8\)-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.

Reviewer: U.Göhner (Leonberg)

MSC:

65T50

Numerical methods for discrete and fast Fourier transforms

Keywords:

fast algorithms; discrete cosine transforms; scaling; quantization