lanczos3 vs 3-pole RM detail

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

Detail of defects in the stop-band ripple of 3-lobe Lanczos and cascaded running-mean filters. Overall frequency response:

It should be noted that this is the conventional magnitude plot showing only the size of the response, not it’s sign. In each case the first lobe is, in fact, negative ie. the signal gets inverted.

The successive peaks alternate positive/negative.

It can be noted that while the Lanczos has a much better large scale response, it does suffer from some “ringing” artefacts.

The first triple running-mean uses coefficients suggested by Vaughan Pratt where each stage’s window is 1.2067 time shorter (or as near as this can be realised with the granularity of the data).

This option aims to minimise the overall sum of the deviations.

The disadvantage is that the negative lobes not only represent leakage of part of the signal that it was intended to remove but that it is also inverted. This is a corruption of the data was well as simple leakage.

The asymmetric triple running mean aims to minimise the negative lobes at the cost of accepting a slightly higher second (positive) lobe.