  In this paper we revisit the classical problem of estimating a signal as it
impinges on a multi-sensor array. We focus on the case where the impinging
signal's bandwidth is appreciable and is operating in a broadband regime.
Estimating broadband signals, often termed broadband (or wideband) beamforming,
is traditionally done through filter and summation, true time delay, or a
coupling of the two. Our proposed method deviates substantially from these
paradigms in that it requires no notion of filtering or true time delay. We use
blocks of samples taken directly from the sensor outputs to fit a robust
Slepian subspace model using a least squares approach. We then leverage this
model to estimate uniformly spaced samples of the impinging signal. Alongside a
careful discussion of this model and how to choose its parameters we show how
to fit the model to new blocks of samples as they are received, producing a
streaming output. We then go on to show how this method naturally extends to
adaptive beamforming scenarios, where we leverage signal statistics to
attenuate interfering sources. Finally, we discuss how to use our model to
estimate from dimensionality reducing measurements. Accompanying these
discussions are extensive numerical experiments establishing that our method
outperforms existing filter based approaches while being comparable in terms of
computational complexity.
