Describe › Signal & numerical

Data smoothing (Savitzky-Golay / MA / LOWESS)

Data smoothing overlays a de-noised curve on a raw series using Savitzky-Golay, a moving average or LOWESS, and reports the residual RMSE.

What is Data smoothing (Savitzky-Golay / MA / LOWESS)?

Smoothing separates signal from noise. A moving average is the simplest low-pass filter but blunts peaks. Savitzky-Golay fits a low-order polynomial in a sliding window, so it suppresses noise while preserving peak height and width — the standard in spectroscopy. LOWESS is a robust locally-weighted regression that adapts to curvature and tolerates outliers.

The window (odd) sets the smoothing scale: wider removes more noise but risks flattening real features. The residual RMSE (raw − smoothed) quantifies how much variation was treated as noise.

When should I use Data smoothing (Savitzky-Golay / MA / LOWESS)?

  • Cleaning noisy instrument or sensor data before peak/derivative analysis.
  • Producing a visually smooth trend line without fitting a global model.

What data does it need?

One numeric series (row order = order) + method + window (odd) + polynomial degree (Savitzky-Golay) or span (LOWESS).

What does it report?

The smoothed curve overlaid on the raw data plus the residual RMSE.

What does it assume?

  • Even sampling is assumed for the moving-average and Savitzky-Golay filters.
  • The window must be smaller than the features you want to keep.

How do I interpret the result?

Compare the smoothed curve to the raw data — if genuine peaks are being flattened, shrink the window or use Savitzky-Golay over a moving average.

See also

References

  • Savitzky & Golay (1964). Smoothing and differentiation of data by simplified least squares procedures. Anal. Chem. 36.
  • Cleveland (1979). Robust locally weighted regression and smoothing scatterplots. JASA 74.