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The impact of quantization noise on a signal whose rate is to be estimated using a FIR differentiator is analyzed, concentrating on the important constant-rate case in order that the filter be optimized for systems with low-frequency rates of change. Formulae for the mean-squared error of the filter, the corresponding spectral characteristics, and general formulae governing the filter coefficients are derived. The characteristics of four specific differentiators, including a representativedoi:10.1109/78.960418 fatcat:eaf2jxvzunh5rofro7vpntnxem