Design of fractional delay filters using convex optimization

Fractional sample delay (FD) filters are useful and necessary in many applications, such as the accurate steering of acoustic arrays, delay lines for physical models of musical instruments, and time delay estimation. This paper addresses the design of finite impulse response (FIR) FD filters. The problem is posed as a convex optimization problem in which the maximum modulus of the complex error is minimized. Several design examples are presented, along with an empirical formula for the filter order required to meet a given worst case group delay error specification.