Practical considerations in optimal filtering of TES signals

Transition edge sensors (TES) currently under development for X-ray astronomy exhibit a non-linear energy response and signal-dependent noise statistics. We present a large-signal model of a TES microcalorimeter operating with electrothermal feedback, which includes noise sources. This is then used to simulate the pulse shape and the non-stationary noise statistics. A new methodology is developed to obtain the optimum noise filter at any energy and this is compared with the performance of a single filter of a fixed shape. It is shown that, although the energy resolution degrades with increasing energy, good performance can be maintained even when the detector saturates. There are practical difficulties with implementing an optimum filter, which are discussed. As the resolution only has a second-order dependence on the filter shape, the shape can depart significantly from the optimum with only a small effect on performance. This is demonstrated by an example, and an algorithm is suggested for applying these quasi-optimum filters to real data.