Savitzky–Golay smoothing filter

The Savitzky–Golay smoothing filter is a type of filter first described in 1964 by Abraham Savitzky and Marcel J. E. Golay.^[1]

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The Savitzky-Golay method essentially performs a local polynomial regression (of degree k) on a distribution (of at least k+1 equally spaced points) to determine the smoothed value for each point. Methods are also provided for calculating the first up to the fifth derivatives.

The main advantage of this approach is that it tends to preserve features of the distribution such as relative maxima, minima and width, which are usually 'flattened' by other adjacent averaging techniques (like moving averages, for example).

The paper that the filter appeared in is one of the most widely cited papers in the journal Analytical Chemistry^[2] and is classed by that journal as one of its "10 seminal papers" saying "it can be argued that the dawn of the computer-controlled analytical instrument can be traced to this article".^[3] Savitzky and Golay's original paper contained several typographical errors that were subsequently corrected by Steinier, Termonia, and Deltour.^[4]

See also Numerical smoothing and differentiation

References

1. ^ A. Savitzky and Marcel J.E. Golay (1964). Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Analytical Chemistry, 36: 1627-1639. doi:10.1021/ac60214a047
2. ^ 75 Most Cited Publications. Analytical Chemistry. American Chemical Society (2004). Retrieved on 2007-03-30.
3. ^ 10 Seminal Papers. Analytical Chemistry. American Chemical Society (2004). Retrieved on 2007-03-30.
4. ^ Jean Steinier, Yves Termonia, Jules Deltour (1972). Smoothing and differentiation of data by simplified least square procedure. Analytical Chemistry, 44(11): 1906-1909. doi:10.1021/ac60319a045