A new method for LMS synthesis of optimum finite impulse response (FIR) filters with arbitrary time and frequency constraints and noises

We present a new general method for calculating the optimum filter for high resolution nuclear spectroscopy with assigned time domain constraints (e.g. finite duration, flat top, peaking time, zero area, etc.), and in presence of any kind of noise or disturbance. The method is fully developed. It can be easily implemented into DSP based processors and it can be used as a tool for optimising any configurable digital signal processing spectroscopy set-up in its digital filter section. The method is validated through simulations and experiments.