Optimal design of fractional delay filters

Fractional delay filters are those that are designed to delay the input signals by a fractional amount of the sampling time. They are widely used in digital communications, speech processing, digital modeling of musical instruments, etc. Since the delay is fractional, the intersample behavior of input signals become crucial. While the conventional design bases itself on the full band-limiting assumption, the present paper applies the modern sampled-data H^∞ control which aims at restoring the intersample behavior. It is shown that the optimal design problem is reducible to a norm-equivalent discrete-time problem. A numerical example is shown to illustrate the advantage of the proposed method.