  Fractional delay filters are digital filters to delay discrete-time signals
by a fraction of the sampling period. Since the delay is fractional, the
intersample behavior of the original analog signal becomes crucial. In contrast
to the conventional designs based on the Shannon sampling theorem with the
band-limiting hypothesis, the present paper proposes a new approach based on
the modern sampled-data H-infinity optimization that aims at restoring the
intersample behavior beyond the Nyquist frequency. By using the lifting
transform or continuous-time blocking the design problem is equivalently
reduced to a discrete-time H-infinity optimization, which can be effectively
solved by numerical computation softwares. Moreover, a closed-form solution is
obtained under an assumption on the original analog signals. Design examples
are given to illustrate the advantage of the proposed method.
