Optimization of digital filters for the detection of trace elements in EELS. III--Gaussian, homomorphic and adaptive filters

This paper is the third part of a series of papers dealing with the development of digital filters for the extraction of information from electron energy loss spectra, when the signal-to-background is very weak, as it is the case for elements in weak concentration. Three new filtering approaches are investigated: the use of high-order derivatives (typically, the fourth order derivative of a Gaussian), the use of homomorphic filtering (working on logarithmically-transformed spectra) and the use of adaptive filtering, taking into account the local background shape. These signal processing methods are applied to real spectra to demonstrate and comment their effects in three different cases of signal and background shapes related to calcium, phosphorus and boron detection in definite thickness organic matrix.