An optimal design of the extrapolated impulse response filter with analytical solutions

The extrapolated impulse response (EIR) filter design based on principal component analysis (PCA) generally performs better than the non-optimal type of the traditional EIR filter design. However, no optimality was proposed in the EIR design. In this paper, an understanding of the EIR technique from the perspective of linear representation is presented. Based on the understanding, a technique for the design of the EIR filter is proposed. The proposed design is optimal in the optimal-linear-representation sense in the sequence domain. The solution set of our proposed design is theoretically derived. Within the solution set, a solution with the sub-lowest coefficient sensitivity (CS) is analytically obtained. Provided the scale factors are calculated using our proposed technique, the design of the EIR filter based on PCA (PCA-EIR) can be proved to be a solution within the solution set. Simulation experiments validate our proposed EIR technique. Our proposed EIR technique performs as well as the PCA-EIR technique with respect to the frequency response and (or) the implementation complexity. With respect to the CS, our proposed EIR technique is much better than the PCA-EIR technique. ► We present an optimal design of the extrapolated impulse response (EIR) filter with analytical solutions. ► The presented design is optimal in the optimal-linear-representation sense in the sequence domain. ► An optimal solution set is analytically given. ► How to choose a solution that has the sub-lowest coefficient sensitivity from the optimal solution set is given. ► Simulations validate our proposed design.