Design rules for optimization of digital spectrometers

A well-designed digital spectrometer permits to implement the optimal-filter weighting function, so optimizing the spectral quality of the measurements. Nonetheless the optimal-filter theoretical performance is difficult to attain owing to the effects related to (i) the residual aliasing in the analog-to-digital conversion, which emerges as a high-frequency perturbation of the filter weighting function, and (ii) the contribution of the quantization noise to the overall system noise. In this paper it is shown that, given a resolution of the analog-to-digital converter, a minimum for effects (i) and (ii) exists, which permits to optimize the performance of the system. Such minimum is obtained by an accurate setting of the anti-aliasing filter bandwidth, and depends also on the required weighting-function width. The design figures which permit to achieve such an optimization will be presented. A procedure of noise data fitting will be also shown, which permits to disentangle the various noise components, including the quantization noise. This latter procedure may be used as a diagnostic tool to check the proper operation of the spectrometer.