Digital Penalized LMS method for filter synthesis with arbitrary constraints and noise

A new method to calculate optimum digital filters for applicative fields requiring high resolution measurements, such as nuclear spectroscopy, is presented. This method easily works in experimental measurement setups, as optimum filter is synthesized with regard to the assigned time and frequency domain constraints (e.g. finite duration, flat top, peaking time, zero area, etc.) and by taking into account the real environmental noise or disturbance present in the system and identified from data sets of straightforward signal acquisitions. The method is fully developed and compared with other state of the art techniques for synthesis of optimized numerical filters. It can be easily implemented into DSP based processors and can be used as a tool to optimize the digital filter section of reconfigurable processing setups.