Techniques for avoiding sign-extension in multiple constant multiplication

In this work we consider three different techniques for avoiding sign-extension in constant multiplication based on shifts, additions, and subtraction. Especially, we consider the multiple constant multiplication (MCM) problem arising in transposed direct form FIR filters. The main advantage of avoiding sign-extension is the reduced load of the sign-bits. Furthermore, the complexity is slightly reduced as full adders are replaced by half adders or full adders with one constant one input. The proposed techniques can be applied independent of which algorithm was used to solve the MCM problem.