Digital interpolation beamforming [R. Pridham and R. Mucci, J. Acoust. Soc. Am. 63, 425–433 (1978)] permits a reduction in A/D conversion rate, telemetry bandwidth, and memory throughput, relative to nearest-sample-selection beamforming, at the expense of an increase in arithmetic operations. However, conventional synthesis techniques for the up/down sampling interpolator filters used in such a beamformer are typically based on specifications which are not directly related to the beamformer response; thus an excessive computational rate may result. This paper describes an alternative approach to the synthesis of arithmetic digital beamformers, involving the design of the individual digital filters which perform delay interpolation on the hydrophone signals for a given steering direction. It is shown how to set specifications on the amplitude and phase frequency responses of these filters based on beam pattern tolerances. Optimal digital interpolator synthesis methods then yield computationally efficient beamformer solutions. Examples are presented for several array geometries.