Design-chart aided optimization of digital spectrometers

Digital spectrometers permit implementation of 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 (1) the finite resolution of the analog-to-digital converter (ADC) and (2) stray high-frequency oscillations in the processor weighting function. In this paper, it is shown that for a given resolution of the ADC, a minimum for effects (1) and (2) exists, which permits one to optimize the performance of the system. Such a minimum is obtained by an accurate setting of the analog prefilter bandwidth and depends also on the required weighting-function width. Design charts that permit one to achieve such an optimization will be presented. A procedure of noise data fitting will be also shown, which disentangles the various noise contributions, including the quantization noise. This latter procedure may be used as a diagnostic tool to check the proper operation of the spectrometer.