I recently have encountered very short time signals (from three to 12 samples, typically). They appeared for instance in small time frames in engine simulation that should be extrapolated in a robust manner, or gaz measurements taken for instance at $t_0 = 0$ (seconds), $t_1 = 5$, $t_2 = 10$, $t_3 = 20$, $t_4 = 50$, $t_5 = 100$. The idea behind this time sampling is that the signal should rise or fall, and may reach some steady-state. Such data cumulates caveats:
- Very short,
- Sometimes corrupted by one missing data, or one potential outlier,
- Uneven sampling.
Traditional tools (Fourier, correlation, fitting) appear of limited use, and are probably unusable. Yet I would like to:
- describe those signals with few robust parameters,
- estimate offsets and delays between two signals,
- cluster them with shape similarity.
I for instance would like to detect "V-shaped" short signals that first go down then up, obtain a location estimator for the wedge, and separate them from monotonous or down-then-flat signals.
So far, I am performing tedious 3- or 4-point linear or parabolic fits, estimate residues and dispersion to select "a best model", with standard quadratic or robust quantile estimation. My questions are:
- Is there recommended literature on very-short signal processing?
- Would users share their best-practice experience on such signals, that ought to be processed?