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I am having fun with Savitzky-Golay (aka H-P, W-H) and I am bumping into limits of the filter. It makes me want a better filter.

Is there a filter that adjusts filter order based on "slope" but that also, like Savitzky-Golay filter, has forms that lead cleanly to nice estimates of derivatives for the data?

It sounds like a contradiction: using slope to control knobs in estimating slope. My hope is that it has at some point sounded like a mathematically interesting contradiction, and that someone found a reasonable solution for it.

Here is my pain (see images):

  1. when the slope is low, the filter doesn't remove the effects of
    discretization.
  2. if the window is any wider then the filter doesn't handle periods of oscillation.
  3. if the order is lower, the linear area is handled well but the sinusoidal loses amplitude
  4. when the order is higher the filter doesn't remove the effects of discretization

Slow slope with high order filter (notes Gibbs effect at plateau edges: filter adds noise): enter image description here

Sinusoidal with high order filter: enter image description here

Slow slope with low order filter (no ringing):
enter image description here

Sinusoidal area with low order filter (loses signal):
enter image description here

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