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Abstrtrct-Digital timedomain beamforming requires that samples of the sensor signals be available at a sufficient rate to realize accurate time delays for beam steering. For many applications, this input rate, which may be significantly higher than the Nyquist rate required for waveform reconstruction, places stringent requirements on A/D converter hardware and transmission b b l e bandwidth. Recently, a technique referred to as digital interpolation beamforming was introduced which greatly relaxes the sampling requirement and provides substantial hardware savings through more flexible design options. In this approach, the sensor channels need only be sampled at a rate which satisfies aliasing requirements.The vernier beamdelay increments are then synthesized using digital interpolation which can be implemented at the beamformer input or output to minimize digital processing complexity.Previously, this concept was presented for the case of "low-pass"signals. This paper extends this work by examining the relationship between interpolation and beamforming for the important class of "bandpass" signals. Specifically, sampling methods are discussed whereby the original waveform can be reconstructed from samples taken at a rate consistent with the bandwidth of the bandpass signal.Beamformer implementations are presented which utilize these bandwidth-sampling techniques in conjunction with interpolation and which compute beam output points at the generally low rate dictated by the signal bandwidth. The interpolation beamformer achieves timedelay quantization (beam-steering accuracy) independent of both the input and output sampling rates. This approach generally requires less hardware than conventional procedures. Interpolation fdter characteristics dictated by the bandwidth-sampling procedure are described and efficient methods of implementation employing nonrecursive digital bandpass and low-pass fiiters are presented.

For many sonar applications, the sensor outputs of a hydrophone array are sampled at a rate significantly higher than that required for waveform reconstruction when digital beamforming is used. The reason for this is that the number of synchronous, or ’’natural,’’ beampointing directions is proportional to the beamformer input rate. This paper presents an implementation of a digital beamformer that achieves the desired synchronous beams while minimizing the sensor channel sampling rate requirement. The technique employs zero padding of sensor data followed by digital interpolation filters to achieve vernier beamformer delays. Interpolation filtering can be done either at the beamformer input or output to minimize processing requirements. The resulting structure realizes a hardware savings since both A/D converter and cable bandwith requirements can be traded off against digital processing complexity to achieve an optimal partitioning.

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INPUT Bo 70i ! "t ,i * 20 40 €a 80 1 0 0 120 1 4 0 $ 6 0 FRMUENCY Hz Fig. 3. Measured and theoretical frequency Rspons of ZGo).(The Q of the response is indicative of the proximity of the poles to the axis.) It should be noted that this particular realization may be unstable due to the large open loop gain at high frequencies. Careful desigq using conventional Bode techniques, can ensure stability by the addition of a "roll-off" capacitor C, as shown in Fig. qa). The measured response, given in Fig. 3, agrees closely with (4). The Q of this response is approximately 20 and is limited by the h i t e gain and nonzero phase shift of the transistors.The applications of this type of network are the subject of continuing work. Preliminary investigations have indicated that the problem of simulating floating inductors in low-pass LC ladder filters may be overcome by replacing the floating inductors by resistors and the shunt capacitors by impedances of the type given in (3). hactical circuit realizations, using this method, are being investigated and it will be shown that many LC driving point and transfer immittances may be simulated. The results of this work will be reported at a later date.