Performance Comparison of FIR Low-Pass Digital Differentiators for Measurement Applications

Low-pass Digital Differentiators (LPDs) are adopted in a variety of measurement and testing applications. However, a clear performance analysis of different solutions is seldom reported in the scientific literature. Maybe this is due to the lack of criteria to analyze their behavior on a common basis. In this paper, the passband and stopband features of two families of Finite Impulse Response (FIR) LPDs (namely those resulting from the classic windowing design method and the so-called maximally-flat differentiators) are purposely analyzed under comparable conditions. In particular, starting from a revised definition of Equivalent Noise Bandwidth (ENBW) adapted to the LPD case, a criterion to compare both types of digital differentiators is proposed for common settings of ENBW and impulse response length. The reported analysis shows that, even if the maximally-flat LPDs exhibit a smoother frequency response within the passband, a negligible magnitude error around DC and the possibility to compute the coefficients using recursive analytical expressions, they are less selective than the corresponding windowing-based differentiators. Moreover, while the stopband attenuation of maximally-flat LPDs is higher, their Root Mean Square (RMS) magnitude response errors within the passband are significantly higher. Last but not least, the maximally-flat LPDs suffer from two crucial problems, i.e. finite (and potentially coarse) bandwidth resolution and poor numerical stability, as the filter order grows.