Analysis on word length assignment for integer DCT considering colored spectrum

While JPEG 2000 adopts the integer wavelet transform to attain "lossless" coding of images, the DCT based "lossy" coding still prevails in various fields of video communication technologies. This paper investigates the integer DCT that can implement "lossless" coding of images maintaining compatibility to the "lossy" DCT coding. So far, we have assigned optimum word length to each of multipliers in the integer DCT assuming colored spectrum of input image signal. However it is remained unknown that A) Is the assigned word length robust to change of input signal\´s characteristics? B) Does it depend on structure of the transform? This report is intended as an investigation of theoretical analysis to answer these questions.