This work proposes a new representation of the gradient system transfer function (GSTF) based on finite impulse response (FIR) filters. FIR filters can represent arbitrary gradient functions but are not used because of their computational complexity. The proposed method represents the GSTF as a set of average coefficients and their durations. Input signals are represented as sums of signals for the same durations. On an update step, only two signals are accessed for each duration. Therefore, as confirmed experimentally, the proposed method can process arbitrary gradient functions in acceptable computational time, without using infinite impulse response (IIR) filters.