Binomial smoothing filter: A way to avoid some pitfalls of least-squares polynomial smoothing

Abstract

Some pitfalls of least‐squares polynomial (LSP) smoothing (better known to analytical chemists as Savitzky–Golay smoothing) are demonstrated and discussed, as well as some remedies. For instance, smoothing by long LSP sequences leads to transmission zeros, phase reversals, and overshoots that may be objectionable in some applications. An alternative method, the binomial smoothing filter, is described and some of its properties are presented. It is shown to be preferable to LSP smoothing in many cases. It is faster, better behaved in both the data and the frequency domains for many applications, and simpler to use and to program or to implement in hardware. Finally, the action of a filter of a given order is easy to predict.