Predictive FIR filters with low computational complexity

New families of finite-impulse-response (FIR) digital filters with low computational complexity are presented. The filters are extensions of the recursive running sum. Each family of filters predicts points along a characteristic polynomial. Closed-form equations are given in both time- and frequency-domain for filters corresponding to first- and second-order polynomial models. Block diagrams for efficient implementation structures are given. The first-order predictive filters require three multipliers and five adders, and the second-order predictive filters require five multipliers and twelve adders, irrespective of the filter length. The filters exhibit low-pass characteristics with the passband shape controllable by a single parameter. The frequency and phase responses are discussed. A design example is given showing how the filters can be used as building blocks to obtain effective linear-phase low-pass filters