Sliding Time Window Function

[northern_flicker]

Dear Forum

This problem is quite similar to a moving average, but it has two differences, which I am struggling to overcome. It is applicable to a heterogeneous time series with dependent x and y values, i.e., {time, x, y}, where the temporal variations in x and y are of interest.

1) It would be preferable to have a sliding window based on a time interval rather than the number of data, e.g., 0.5 s, 5 min., 50 years, etc.
2) Instead of a moving average I would like to apply some expression over the moving time interval that uses both x and y, e.g.,

Total[Cos(x)*Sin(y)]/Total[Cos(x)*Cos(y)]

A fresh approach would be much appreciated

[Vince Virgilio]

I have something which might suit. I use it for sliding window averages over non-uniformly sampled time series.

binWin[seq_, f_, intervals_, g_:Identity] :=
Module[{sorted = SortBy[seq, f], order = Ordering@intervals[[All, 1]]},
Function[{tLo, tHi},
sorted = Drop[sorted, LengthWhile[sorted, f@# < tLo &] ];
g @ TakeWhile[sorted, f@# < tHi &]
] @@@ intervals[[order]] // #[[Ordering@order]]&
];


'seq' is the list of (x,y) pairs, where y may be scalar or vector. 'f' picks the sort-by or key field (say, time). Usually, it is 'First'. 'intervals' is a sequence of time (key) intervals which may overlap. And 'g' is your reduction, which is applied to each window (bin). binWin will take unordered series and window specs and return the windowed results ordered according to the lower bound of the intervals.


I think it's fairly performant. But I'd appreciate any improvements.

Vince