A Wiener Filter Based Band-Pass FIR Differentiator with Zero Delay

The calculation of signal derivatives is a sensitive operation in digital signal processing. This is due to the high pass nature of the derivative operation and the subsequent noise amplification. Bandlimited differentiator designs based on FIR approximations are therefore commonly used. Another prominent technique is Savitzky-Golay-filtering to design FIR differentiators. However, all of these techniques introduce a temporal shift by the (constant) group delay of the odd FIR filters. In this work we present a FIR differentiator design for band-pass signals based on a Wiener filter approach. Therefore, the differentiation task is treated as a signal estimation problem, which leads to a delay free FIR differentiator. The design specifications for the filter, e.g. the bandwidth, are formulated in the frequency range. The properties and performance of the approach are presented by means of comparative simulation studies.