ds. input and the resulting difference, the prediction error, is requan- tised with fewer bits and with a non-linear law. The non-linearity is 57.4.5 Transform Coding such that small differences, which occur in low detail regions, are coded accurately whereas more distortion is allocated to large Transform Coding is another method to exploit the similarities of differences generated in high detail areas. pels which are in the same neighbourhood of space or time. The The DPCM output is thus a sequence of short code words which most commonly used transform is the two dimensional Discrete index the quantiser levels. The decoder converts each index to the Cosine Transform (DCT), applied to a rectangular spatial block of relevant representation level and adds it to the prediction to recon- m by n pels. The forward transformation is computed according to struct each output sample. So that the encoder and decoder remain Equation 57.3 and the inverse (IDCT) by Equation 57.4, where x,y in track it is essential that the encoder uses only information also are spatial coordinates in the pel domain and u,v are coordinates in available at the decoder. Hence the encoder contains the essential the transform domain. C(u) and C(v) are given by Equations 57.5 parts of a decoder SO that it uses a reconstructed version of the and 57.6 respectively. previous pel rather than its original input value. The prediction can be the pel immediately to the left on the same scan line in which case the delay is one sample period. The delay can be one TV line in which case the pel immediately above is used. The pel in the same spatial position in the previous picture is the result of making the delay equal one picture period. The optimum (57.3) delay depends on the localised picture content. Simple DPCM coders utilise a fixed delay or a weighted combi- nation of pels from fixed delays. More sophisticated versions dy- namically select the optimum prediction and either explicitly E(u)C(v)F(u,v) indicate the choice in the coded bit stream or use rul