  In this work we demonstrate the use of autoencoder networks for rapid
extraction of the signal parameters of discretely sampled signals. In
particular, we use dense autoencoder networks to extract the parameters of
interest from exponentially decaying signals and decaying oscillations. Using a
three-stage training method and careful choice of the neural network size, we
are able to retrieve the relevant signal parameters directly from the latent
space of the autoencoder network at significantly improved rates compared to
traditional algorithmic signal-analysis approaches. We show that the achievable
precision and accuracy of this method of analysis is similar to conventional,
algorithm-based signal analysis methods, by demonstrating that, the extracted
signal parameters are approaching their fundamental parameter estimation limit
as provided by the Cram\'er-Rao lower bound. Furthermore, we demonstrate that
autoencoder networks are able to achieve signal analysis, and, hence, parameter
extraction, at rates of 75 kHz, orders-of-magnitude faster than conventional
techniques with equal precision. Finally, we explore the limitations of our
approach, demonstrating that analysis rates of $>$200 kHz are feasible with
further optimization of the transfer rate between the data-acquisition system
and data-analysis system.
