Closed form variable fractional delay using FFT with transition band trade-off

In earlier paper, a conjugate symmetric frequency response has been presented to design the variable fractional delay filter by FFT, and has been proved to associate with the windowed sinc filter. However, this earlier method has no transition band design consideration. Therefore, in this paper, the trade-off between the transition band width and Gibbs phenomenon ripples is discussed, and an improved closed form design with additional transition band samples is introduced to reduce Gibbs phenomenon ripples. The proposed improved fractional delay method can also be efficiently realized by FFT using the tunable fractional delay parameter and transition band weighting factor. Several comparisons between the earlier method and the proposed improved method are also demonstrated. By measuring the largest peak ripple value in magnitude responses, our proposed method can achieve 9.43 times peak ripples reduction than the earlier method.