A multiscale polynomial filter for adaptive smoothing

The effectiveness of Savitzky–Golay type symmetric polynomial smoothers is known to be strongly dependent on the window size. Many authors note that selection of the appropriate window size is essential for achieving the correct trade-off between noise reduction and avoiding the introduction of bias. However, it is often overlooked that, in the case of non-stationary signals, the optimal window size will vary with the dynamics of the signal. A multiresolution approach is outlined, along with criteria for varying window size with respect to translation, based on evaluation of the residuals of the smoothed data in the local region. Adaptive window polynomial smoothing is shown to be superior to fixed window smoothing for a test signal at various signal-to-noise ratios.