Low coefficient complexity approximations of the one dimensional discrete cosine transform

Abstract

A method for the design of arbitrarily exact Discrete Cosine Transform (DCT) approximations that permits perfect reconstruction using fixed point arithmetic is presented. Simple quantization of floating point precision coefficients typically leads to DCT approximations which fail to meet the coding gain, Mean Square Error (MSE), and coefficient complexity (number of coefficient adders and subtractors) specifications. It is shown that it is possible to design DCT approximations with near optimal coding gains that meets the MSE and coefficient complexity requirements. Finite precision effects are discussed for these DCT approximations.