I am looking at some suggested filters for tidal data but am having trouble understanding the notation. For example, Godin (1972) suggests a low-pass filter for tidal data that is a combination of 24-hour and 25-hour averages, using the notation

$$ \frac{A_{24}^2}{24^2}\frac{A_{25}}{25} $$

My understanding of this filter is that it consists of a 25-hour average and two 24-averages (one leading, one lagging). However, I don't understand how the notation communicates this.

Another filter, referred to as the "even species filter", has the notation

$$ \frac{1}{16}A_{12}^2A_{13}^2 $$

Which I presume is using two 12-hour and 13-hour averages each, but I don't know the orientation.

Any help with understanding this notation would be appreciated.

Godin, G., 1972. The Analysis of Tides. University of Toronto Press, 264 pp.


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