Optimal design of fractional delay FIR filters without band-limiting assumption

Fractional delay filters are those that are designed to delay the input signals by a fractional amount of the sampling time. Since the delay is fractional, the intersample behavior of the original analog signals become crucial. While the conventional design bases itself on the assumption that the incoming analog signals are fully band-limited up to the Nyquist frequency, the present paper applies the modern sampled-data H^∞ optimization which aims at restoring the intersample behavior without the band-limiting assumption. It is shown that the optimal FIR filter design is reducible to a convex optimization described by a linear matrix inequality (LMI). A design example is shown to illustrate the advantage of the proposed method.