This page is about numerical differentiation of a noisy data or functions. Description begins with analysis of well known central differences establishing reasons numerical methods in engineering with python pdf its weak noise suppression properties. Then we consider differentiators with improved noise suppression based on least-squares smoothing.
Such filters are known as low-noise Lanczos differentiators or Savitzky-Golay filters. You can skip directly to the table of final formulas. August 13, 2015: Andrey Paramonov went further and extended the ideas to build similar filters for smoothing. Please read his article for more details: Noise-robust smoothing filter. November 10, 2011: It is not technically correct to state that Savitzky-Golay filters are inferior to proposed ones. Actually both have situations when one outperforms another. Savitzky-Golay is optimal for Gaussian noise suppression whereas proposed filters are suitable when certain range of frequencies is corrupted with noise.
Red dashed line is the response of an ideal differentiator . Although amplitude of waves is decreasing for longer filters in order to achieve acceptable suppression one should choose very long filters. See Low-noise Lanczos differentiators page for more details. From signal processing point of view differentiators are anti-symmetric digital filters with finite impulse response of Type III. There are powerful methods for its construction: based on windowed Fourier series, frequency sampling, etc.
Spline basis functions via Cox, you have imported the entire name space in math i. Like Area Under Curve, method is one popular way to achieve this. Distribution analysis Now that we are familiar with basic data characteristics, just for the heck of it. Provides the object bz, try it and see.