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A general approach to the design of single-rate fractional-step delay (FSD) filters for array beamforming, based on a state-space formulation, is presented. This approach is applicable to both FIR and IIR implementations. In this approach, state-space realizations of FSD filters can be derived from state-space realizations of parent interpolating filters. The realizations so produced have the property that the fractional-step delay is determined solely by the B (input coupling) matrix. The A (system) and C (output coupling) matrix operations are independent of the fractional-step delay, and thus can be shared by all array element channels. All FSD beamformers are subject to spurious spatial response lobes generated by aliasing in the interpolating filter. However, these spurious lobes can be effectively suppressed by appropriate design of the magnitude response of the interpolating filter. If the magnitude response of the interpolating filter is chosen so that the spurious sidelobes are effectively suppressed, then although the phase response of the interpolating filter will affect the temporal response of the system, it will have no effect on the spatial response of the array; i.e., it is not necessary to have linear phase response in the interpolating filter to obtain ideal beam patterns. Comparisons of computation rates for FIR and IIR implementation of FSD beamformers are presented.