Mean-square-error reduction for quantized FIR filters

Abstract

In the article the author discuss fundamental properties of canonic signed digit (CSD) fixed point representation of numbers. Although properties of CSD format are well known from literature, published proofs are tedious and occupy lot of columns of text. Here the problem has been reduced to the problem of combinatorial number. The tool for this reduction is a "drawer lemma" - lemma about the distribution of identical objects in drawers or holes. Next there is proposed an algorithm for the computation and quantization of canonic signed digit (CSD) coefficients in a constant-coefficient multiplierless FIR filter. The algorithm is proven to be optimal in the mean square error sense. The algorithm is recurrent and unexpectedly simple, so it can be easily implemented inside any mathematical program as MATLAB or MATHCAD