Multiplierless design of linear DSP transforms

Abstract

The last two decades have seen tremendous effort on the development of high-level algorithms for the multiplierless design of constant multiplications, i.e., using only addition, subtraction, and shift operations. Among the different types of constant multiplications, the multiplication of a constant matrix by an input vector, i.e., the constant matrix-vector multiplication (CMVM) operation, is the most general case and occurs in many digital signal processing (DSP) systems. This chapter addresses the problem of minimizing the number of addition and subtraction operations in a CMVM operation and introduces a hybrid algorithm that incorporates efficient techniques. This chapter also describes how the hybrid algorithm can be modified to handle a delay constraint. The experimental results on a comprehensive set of instances show the efficiency of the hybrid algorithms at both high-level and gate-level, in comparison to previously proposed methods. © 2012 IFIP International Federation for Information Processing.