  This work presents two novel optimization methods based on integer linear
programming (ILP) that minimize the number of adders used to implement a
direct/transposed finite impulse response (FIR) filter adhering to a given
frequency specification. The proposed algorithms work by either fixing the
number of adders used to implement the products (multiplier block adders) or by
bounding the adder depth (AD) used for these products. The latter can be used
to design filters with minimal AD for low power applications. In contrast to
previous multiplierless FIR approaches, the methods introduced here ensure
adder count optimality. To demonstrate their effectiveness, we perform several
experiments using established design problems from the literature, showing
superior results.
