The implementation of digital fraction delay has found diverse applications in signal processing, leading to extensive research in this area. To improve the accuracy of channel estimation in practice, Fractional Delay Finite Impulse Response (FD FIR) filters have been proposed. This paper presents the implement principle of fractional delay FIR filters. Building upon existing solutions, it makes improvements to the methods of windowed sinc function, smooth transition function, complex general LS design, and maximally flat design: Lagrange interpolation from simplicity, efficiency, and filter performance, particularly in the reduction of Gibbs phenomenon caused by truncation in time domain. The effectiveness of the proposed method is validated through MATLAB simulation and comprehensive magnitude response analysis, which demonstrates that the complex LS design exhibits the best response with a wider passband and almost no ripple or Gibbs phenomenon.