Round-off Error Free Fixed-point Design of Polynomial- Predictive Fir Differentiators

In this paper, we present a novel method for designing polynomial-predictive FIR differentiators for fixed-point environments. Our method yields filters that exactly fulfill the given constraints even with short coefficient word lengths. Under ordinary quantization, either by rounding or truncation, these filters in most cases loose their predictive and/or differentiating properties, making their fixed-point implementations useless. With the method proposed in this paper, the filters are designed so that the desired properties are exactly preserved in fixedpoint implementations. The presented filter design method is based on integer programming (IP) and can be directly applied to any fixed-point FIR design specifications which can be stated in a form of linear constraints on filter coefficients.