Choice and properties of adaptive and tunable digital boxcar (moving average) filters for power systems and other signal processing applications

The humble boxcar (or moving average) filter has many uses, perhaps the most well-known being the Dirichlet kernel inside a short-time discrete Fourier transform. A particularly useful feature of the boxcar filter is the ease of placement of (and tuning of) regular filter zeros, simply by defining (and varying) the time length of the boxcar window. This is of particular use within power system measurements to eliminate harmonics, inter-harmonics and image components from Fourier, Park and Clarke transforms, and other measurements related to power flow, power quality, protection, and converter control. However, implementation of the filter in real-time requires care, to minimise the execution time, provide the best frequency-domain response, know (exactly) the group delay, and avoid cumulative numerical precision errors over long periods. This paper reviews the basic properties of the boxcar filter, and explores different digital implementations, which have subtle differences in performance and computational intensity. It is shown that generally, an algorithm using trapezoidal integration and interpolation has the most desirable characteristics.