  Dynamic Mode Decomposition (DMD) is a widely used data-driven algorithm for
estimating the Koopman Operator.This paper investigates how the estimation
process is affected when the data is quantized. Specifically, we examine the
fundamental connection between estimates of the operator obtained from
unquantized data and those from quantized data. Furthermore, using the law of
large numbers, we demonstrate that, under a large data regime, the quantized
estimate can be considered a regularized version of the unquantized estimate.
This key theoretical finding paves the way to accurately recover the
unquantized estimate from quantized data. We also explore the relationship
between the two estimates in the finite data regime. The theory is validated
through repeated numerical experiments conducted on three different dynamical
systems.
