Optimum filtering in the presence of dominant 1/f noise

Abstract

Optimum step response waveshapes for filtering in high resolution opto-feedback X-ray spectrometer systems in which 1/ f noise is dominant are calculated. The resulting cusps are shown to reduce the electronic noise line width of very good spectrometer systems by approximately 10% at long peaking times. Implementation of such filters by transversal or by time variant methods is discussed and, as an example, it is shown theoretically that for a system with 90.5 eV fwhm electronic noise as filtered with a 7th order pseudo-Gaussian waveshape at τ 0 = 35 μs, the corresponding noise line widths for the optimal cusp and for a particular time variant filter would be 82.5 and 75 eV fwhm respectively.