A comparison of error behaviour in the implementation of the DCT and the ICT

The discrete cosine transform (DCT), being one of the real transforms, suffers from errors due to imperfect representation of its basis components as well as transformed coefficients. Assume that the DCT basis components are perfectly represented. To examine the error due to truncation/rounding of transformed coefficients of two types of transforms, namely, the real and integer transform, the authors first study the error propagation behavior due to inadequate bits allocated to the 1-D order 8 DCT transformed coefficients and then estimate the mean-square error incurred in a statistical approach presented by M. Gugliemo (1986). The integer cosine transform (ICT) (10,9,6,2,9,3) is used to obtain numerical values to compared with those of the DCT. Theoretical results show that the ICT performs much better than the DCT in this aspect. ICT(10,9,6,2,9,3) requires only 4 bits for exact representation of its kernel elements and has a performance very close to the DCT for a Markov-I signal