A General Study on Sampling Frequency Limits for Digital Spectrometer

Choosing a moderate sampling frequency f_s for digital spectrometer commonly relies on experiences. In this paper, we present the effects of f_s on the resolution of digital spectrometers based on optimum filter theory. The ratio of the optimum SNR of digital (discrete) filtration to the optimum SNR of analog (continuous) filtration (eta_D/eta_A) is derived. The lower limits of f_s to achieve different levels of eta_D/eta_A are also calculated, which provides a new selection criterion for f_s other than Shannon theorem. For a RC anti-aliasing filter (AAF), the minimum f_s is required to be 4.7/2piRC to achieve 0.99 of eta_D/eta_A. This ratio is sensitive to the order of the AAFs and slightly dependents on the noise components of the preamplifier. And the analysis on sampling frequency limits for trapezoidal filters is simulated by MARLAB/SIMULINK.