Implementation of programmable multiplierless FIR filters with powers-of-two coefficients

An observation which is useful for hardware implementation of programmable FIR filters with powers-of-two coefficients (2PFIR filters) is made. Specifically, it is shown that the exponents of filter coefficients representable by the canonical signed digit (CSD) code with M ternary digits can be chosen from some subsets of {0,1,...,M-1}. This observation naturally leads to 2PFIR filters with shorter shifters whose length is strictly less than M and, as a consequence, leads to an efficient hardware structure for programmable 2PFIR filtering. In addition, we present some experimental results indicating that the shifters of 2PFIR filters can be shortened further in some cases