  In this work we demonstrate the use of neural networks for rapid extraction
of 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. By 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 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 similar 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.
