lanczos3 vs 3-pole RM

frequency axis is in units of “per year” not “year” as labelled.

Frequency response of 3 lobe Lanczos low-pass filter and three-pole cascaded running mean filters.

The triple running means are near identical on this scale. The small differences are to be found in the detail of the stop-band ripple:

Code to implement the low-pass Lanczos filter:

Code for triple running mean here:

The Lancos filter provides a much sharper transition and unlike the gaussian and running-mean filters does not start attenuating straight away, providing a good, relatively flat pass-band.

This comes at a price, in that getting a sharper response requires more data points and thus a larger filter window.

In this case, it results in about 6.3 years truncation at each end of the dataset compared to 22 months for the triple running means.