Design and optimisation of regression-type small phase shift FIR filters and FIR-based differentiators with optimal local response in LS-sense

摘要

The design of finite impulse response (FIR) filters and FIR-based differentiators is a popular topic in the field of digital signal processing. FIR filters/differentiators are characterised by a filtering architecture that does not include a feedback loop. Therefore, they are stable and have a relatively simple design, and most importantly, they can yield a filter with a linear phase diagram. Nevertheless, the FIR filter design methods reported in the scientific literature lead to a filter architecture that causes a transport delay or a nonlinear phase shift in the implementation environment. This limits the applicability of FIR filters/differentiators, e.g. in closed-loop control or real-time state estimation. In this paper, a method for FIR filter and FIR-based differentiator coefficient design is presented. The coefficients of the FIR filter and FIR-based differentiator are designed such that the FIR architecture results in a convolution leading to a locally optimal response in the least-squares sense. Thus, the FIR architecture response is characterised by an extremely small phase shift for the pass-band of the designed architecture. This feature results in a higher-order FIR architecture compared with the conventional design methods. In the proposed method, the delay caused by the FIR architecture is minimised by coefficient determination. Therefore, when the method is applied to a known FIR architecture, it causes a shorter delay than all other methods of coefficient determination.