Gain correction for nearly optimal variable fractional sample delay filter design

One of the most numerically efficient digital filter design methods is the window method. This makes the window approach well suited for variable fractional sample delay (VFSD) filter implementation which requires frequent impulse response recalculation. On the other hand, if high performance filters are required, window selection is usually problematic. That is why the use of symmetric window extracted from the optimal filter is investigated in this paper. Such single window, extracted for some arbitrary delay, can be used to implement nearly optimal VFSD filter. However, with the delay change the gain of the designed filter changes too, which significantly deteriorates filter performance and must be corrected. As we have demonstrated, the proper gain correction leads to nearly optimal FSD filter design allowing for nearly optimal numerically efficient implementation of VFSD filter. Two cases for different optimality criteria, minimax (Chebyshev) and least squared error, have been discussed in this paper.