Implementation of optimal filters for pulse height measurement from non-linear detectors with non-stationary noise

Transition-edge sensors currently under development for X-ray astronomy exhibit a non-linear energy response and signal-dependent noise statistics. Previous papers have derived equations for optimal filters for the estimation of the X-ray energy. In this paper, we summarise these results and consider the application of these filters to detector signals. We show that the optimum resolution cannot be achieved in practice, and analyse alternatives which come close to the optimum. We then develop an algorithm for interpolating the filters for an arbitrary energy, given a set of filters at known calibration points. Estimates of the computational requirements indicate that real-time processing should be possible with quite modest resources. The methods described here can be applied to any similar non-linear detector system.