전 디지탈 복조를 위한 다항식 보간필터의 해석 및 그 효율적 구현

Abstract

Interpolation filters are widely used in symbol timing recovery system to interpolate new sample values at arbitrary points between the existing discrete-time samples, and can be implemented using the well-known Farrow structure whose coefficients are obtained by solving an optimization problem. In this paper, we first analyze a polynomial interpolation filters (PIF) in an algebraic way and show that PIF with non-symmetric coefficients can be transformed into PIF with symmetric one by the proposed axis transformation method. In addition, we propose an efficient way of further reduction of arithmetic computation in PIF implementation based on the analysis of constraints which is used for optimization. We start with the analysis of optimization constraints and derive some features that the resulting filter coefficients have. The features are directly appicable to both PIF with non-symmetric coefficients and PIF with symmetric coefficients, and thus leads to a more efficient PIF implementation. Implementation examples are included, illustrating the efficiency of the proposed technique.