Novel generalized optimal fractional delay filter design for navigational purposes

A novel generalized method is proposed for flexibly designing fractional-delay (FD) FIR-type filters which are of the best feasible quality implying a high-accuracy, a fast-adjustability and a low-latency. The FD filters are meant for Nyquist signal reconstruction, not only in amplitude, but specifically, in time under preservation of the attractive linear-phase property. Since the method offers the least number of mathematical operations per coefficient determination ever, namely three (addition, subtraction and division), the method is typically well-suited for software applications. Only by the unique choice of a surprisingly simply staircase-like windowing of the impulse response sequence of the ideal interpolator, followed by a normalization, the frequency and phase delay responses of the best feasible quality originate according to the “equiripple” or, as a special case, to the “maximally-flat” (Lagrange). The method highly benefits allpass implementations also. In addition to applications in the navigational field (GPS, LORAN-C, etc.) many applications are found throughout the whole digital signal processing area, for solving timing problems (tracking, resampling, etc.)