Digital Interpolation Beamforming for bandpass signals

Digital time domain beamforming requires that the output of each hydrophone be sampled prior to beamforming at a rate consistent with the Nyquist criterion for waveform reconstruction. If the sample rate is insufficient for direct realization of the required beam delays, then the desired delays can be achieved by digital interpolation at either the input or output of the beamformer; hence the terminology Digital Interpolation Beamforming [R. G. Pridham and R. A. Mucci, “A Novel Approach To Digital Beamforming,” JASA. 63, 425–434 1978)]. The application of digital interpolation beamforming to bandpass signals is developed. First and second order 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 sampling techniques and hence, operate on data sampled at the generally low rate dictated by the signal bandwidth. The desired beam delays are realized with the appropriate interpolation corresponding to the sampling procedure. This technique is shown to require less hardware than convention techniques. Efficient methods of digital interpolation via Finite Impulse Response (FIR) digital bandpass and lowpass filters are discussed. The beampatterns which result are discussed for a simple line array.