Design of variable fractional delay FIR filter using the high-order derivative sampling method

In this study, a design algorithm for a variable fractional delay finite impulse response (FIR) filter based on piecewise osculating interpolation (POI) is proposed. The proposed algorithm can use higher-order derivative information of the input sampling sequence. To improve the performance of the proposed POI algorithm at high frequencies, two frequency-domain optimization algorithms (including derivative weighted least-squares and derivative minimax algorithm) are proposed. Meanwhile, a one-by-one increase scheme is introduced for optimizing the polynomial orders, such that a given bound is satisfied exactly. Additionally, through derivation of an analytical formula, a two-level Farrow structure is developed to implement the proposed algorithms. As shown, the implementation structure has fixed coefficients and only requires multiplication and addition operations. The proposed algorithms are validated and compared with existing algorithms, and it is shown that the proposed algorithms outperform existing algorithms.