On transform dynamic range in high efficiency video coding

We consider the problem of determining the dynamic range of an inverse transform. An analytic approach is described, and the resulting bound is a function of the bit-depth of the input data and the maximum L₁ norm of the transformation matrix. Furthermore, the analytic approach is refined to account for nonlinearities within a transform due to intermediate, integer conversions. This refinement considers the maximum error introduced by the nonlinearity on the initial, linear bound. The efficacy of the proposed tool is demonstrated by analyzing the inverse transform in the high efficiency video coding (HEVC) standard developed by the JCT-VC.