  Recent sampling theorems allow for the recovery of operators with bandlimited
Kohn-Nirenberg symbols from their response to a single discretely supported
identifier signal. The available results are inherently non-local. For example,
we show that in order to recover a bandlimited operator precisely, the
identifier cannot decay in time nor in frequency. Moreover, a concept of local
and discrete representation is missing from the theory. In this paper, we
develop tools that address these shortcomings.
  We show that to obtain a local approximation of an operator, it is sufficient
to test the operator on a truncated and mollified delta train, that is, on a
compactly supported Schwarz class function. To compute the operator
numerically, discrete measurements can be obtained from the response function
which are localized in the sense that a local selection of the values yields a
local approximation of the operator.
  Central to our analysis is to conceptualize the meaning of localization for
operators with bandlimited Kohn-Nirenberg symbol.
