Fractional delay filter design when sampling rate higher than Nyquist rate

Fractional delay filter design is used to approximate the delay filter exp(-jωD) with a delay D for the full band |ω| < π, using FIR filters or IIR allpass filters. The author shows that the fractional delay filter design is necessary only when sampling is critical, i.e. Nyquist sampling. It is shown that, when the sampling rate is higher than the Nyquist rate, the ideal delay filter exp(-jωD) for the baseband |ω| < π/r only needs to be approximated, where r is the ratio of sampling rate over the Nyquist rate. Numerical simulations are presented to illustrate the theory.