A system for digital filtering includes a set of logic gates, a state storage, and a multiplexer. The state storage includes two or more storage banks and may also include combinatorial logic and/or at least one lookup table. In one application, a filtering operation according to a finite-impulse-response filter coefficient vector is performed without runtime multiplications. Applications to symmetric and antisymmetric filter coefficient vectors are described, as well as applications to filter coefficient vectors of arbitrary odd or even length.