Self-calibration and self-optimization in DSP-based high resolution spectroscopy systems

We propose a mathematical method to automatically evaluate the weights of the digital filters used for high resolution spectroscopy in a mixed analog-digital setup. The optimum filter weighting function WF is obtained from the noise autocorrelation; an ultra-accurate estimate of the singularities of the antialiasing filter is derived from its experimental pulse response. From these data the procedure automatically computes the optimum WF and the digital filter weights. We show that the method provides a much better flatness of the flat top (to within 0.1% of the peak value); a more precise elimination of tails in the WF (to better than 0.1% of the peak value) and a much lower quantization noise (more than a factor 10) at the filter output than other possible methods. It was successfully tested in the generation of trapezoidal and optimum cusp-like WFs even in presence of non negligible 1/f noise. It is run in around one second with no additional hardware.