Digital interpolation beamforming for low-pass and bandpass signals

Abstract

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.

The vector hybrid Wiener filter: Application to super-resolution

“…One-dimensional versions of the scheme in Fig. 1 arise in beamforming [2] and in temporal SR applications [3]. In the latter, several video sequences of the same scene are processed to produce one video stream at a higher frame-rate.…”

“…Our goal is to linearly estimate x(t) given the equidistant pointwise samples of the K signals {y k (t)} K k=1 such that the MSE 2 ] is minimized for every t. To make the derivation general, all we assume in this section is that x(t) and {y k (t)} K k=1 are jointly WSS. We denote their cross-correlation functions by…”

Fast parametric beamformer for synthetic aperture imaging

“…This is achieved using interpolation [46], [47]. Linear interpolation is used to generate samples for time instances that are not integer multiples of the sampling period.…”

Design of a Merged DSP Microcontroller for Embedded Systems using Discrete Orthogonal Transform

“…Therefore, speech data may be sampled at a lower rate for saving the cost of storage and transmission. Interpolation also plays an important role in frequency multiplexing of SSB systems and the digital time-domain beamforming [23] . The theoretical basis for changing the sampling rate by low pass filtering operation is proposed by Schafer and Rabiner [22] and time-domain interpolation using differentiators is introduced by Sudhakar et.…”