  A rigorous formulation of the dynamics of a signal processing scheme aimed at
dense signal scanning without any loss in accuracy is introduced and analyzed.
Related methods proposed in the recent past lack a satisfactory analysis of
whether they actually fulfill any exactness constraints. This is improved
through an exact characterization of the requirements for a sound sliding
window approach. The tools developed in this paper are especially beneficial if
Convolutional Neural Networks are employed, but can also be used as a more
general framework to validate related approaches to signal scanning. The
proposed theory helps to eliminate redundant computations and renders special
case treatment unnecessary, resulting in a dramatic boost in efficiency
particularly on massively parallel processors. This is demonstrated both
theoretically in a computational complexity analysis and empirically on modern
parallel processors.
