The steered response power (SRP) approach to acoustic source localization
computes a map of the acoustic scene from the frequency-weighted output power
of a beamformer steered towards a set of candidate locations. Equivalently, SRP
may be expressed in terms of time-domain generalized cross-correlations (GCCs)
at lags equal to the candidate locations' time-differences of arrival (TDOAs).
Due to the dense grid of candidate locations, each of which requires inverse
Fourier transform (IFT) evaluations, conventional SRP exhibits a high
computational complexity. In this paper, we propose a low-complexity SRP
approach based on Nyquist-Shannon sampling. Noting that on the one hand the
range of possible TDOAs is physically bounded, while on the other hand the GCCs
are bandlimited, we critically sample the GCCs around their TDOA interval and
approximate the SRP map by interpolation. In usual setups, the number of sample
points can be orders of magnitude less than the number of candidate locations
and frequency bins, yielding a significant reduction of IFT computations at a
limited interpolation cost. Simulations comparing the proposed approximation
with conventional SRP indicate low approximation errors and equal localization
performance. MATLAB and Python implementations are available online