Image compression is all the rage these days. and many popular techniques are based on a gimmick called the discrete cosine transform (DCT). It shows up in JPEG (Joint Photographic Experts Group) and MPEG (Motion Picture Experts Group) compression schemes, in techniques for picture phone transmission, and in all four of the proposals the FCC is considering as high definition television standards to replace NTSC. Why is the DCT so wonderful, and in particular, why is it better than the easier-to-compute discrete Fourier transform (DFT)? In this column, I’m going to play around with both these transforms, review their properties, and show an interesting way of thinking about them. © 1993, IEEE. All rights reserved.