An empirical study of minimax-optimal fractional delays for low-pass signals

Abstract

We consider the design of fractional delay (FD) filters for low-pass signals using the minimax-optimality criterion. In particular, we present an empirically derived relationship between the bandwidth, filter order, delay, and peak error, which is useful for parameter selection in design problems. We also present a simple method for rapid online calculation of FD filters with arbitrary shifts. Finally, we present some numerical results comparing these minimax-optimal FD filters with filters derived via the generalized least squares, Lagrange interpolation, and approximate prolate series windowed methods. The simulations suggest that the minimax-optimal delays are competitive with filters designed by other means, and in some cases can significantly outperform them.