On the step response of the DCT

We show that the discrete cosine transform (DCT) is the best orthogonal transform, in terms of energy packing efficiency, for coding input steps of uniformly distributed random phase. Over sufficiently small block sizes, edges in an image can be modeled as such step inputs. This characteristic of the DCT, coupled with its high energy packing efficiency for highly correlated data, helps explain the impressive performance of the DCT for image compression.