Optimum filter for 1f current noise smoothed-to-white at low frequency

This work deals with the synthesis of the optimum filter in nuclear spectroscopy in presence of 1f current noise. Since any experiment has a finite duration, the 1f spectrum at very low frequencies is physically unimportant, while mathematically it forces a zero area constraint in the weighting function. By removing the divergency of the noise spectral density at zero frequency, such a constraint is no more necessary, and finite area shapings are obtained.