Closed-form design of maximally flat FIR fractional delay filters using interlaced sampling method

In this paper, we investigate an implementation of finite impulse response (FIR) fractional delay (FD) filters using interlaced sampling (IS) method. In the design of FIR FD filters with real impulse responses, it is hard for the FD filters to achieve an accurate approximation to the desired frequency response within the high frequency band. The IS structure provides a possible solution to this issue. We solve the closed-form expressions of the impulse responses of the IS structure in maximally flat (MF) error criterion. In addition, we also propose another design in time domain, called the polynomial invariance (PI) method. Using the PI method, we solve the impulse response in closed form and show that the PI design in time domain is identical to the MF result in frequency domain. In the design examples, we compare the proposed design with other existing MF FD filters, and find that the proposed design provides a good approximation to the desired frequency response over the whole frequency band.