Data smoothing using low-pass digital filters

TLDR

The growing use of computer‑controlled data acquisition systems has created a need for general smoothing techniques for digitized experimental data. The goal is to eliminate or greatly reduce high‑frequency noise to obtain an accurate, clean representation of the true phenomenon while keeping the filtering process simple and efficient. Four low‑pass filter design procedures are described, each yielding coefficients for a symmetrical weighting sequence with specified passband width and high‑frequency noise rejection. The filters are illustrated with examples, and Fortran code implementing each design procedure is provided in an appendix.

Abstract

With the increasing use of computer-controlled data acquisition systems which record data in digital form, there has developed a need for techniques which perform a general smoothing process on digitized experimental data. This processing enables the experimentalist to eliminate or greatly reduce the amount of high-frequency noise in order to obtain as accurate and clean representation of the true phenomenon as is consistent with his measurement accuracies. This filtering or smoothing process should be as simple and efficient (least amount of arithmetic per data sample) as is consistent with the experimental situation. The basic concepts of low-pass filters are discussed and four different low-pass filter design procedures are described, each with its own particular smoothing properties. These design procedures give directly the coefficients of a symmetrical weighting sequence having the desired passband width and the desired high-frequency noise rejection. The uses of the filters are illustrated with examples and the fortran code for implementing each of the design procedures is given in an Appendix.