- Savitzky–Golay smoothing filter
The Savitzky–Golay smoothing filter is a type of filter first described in 1964 by
Abraham Savitzkyand Marcel J. E. Golay. [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]
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
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" cite web|url=http://pubs.acs.org/journals/ancham/promo/75th/articles.html |title=75 Most Cited Publications |accessdate=2007-03-30 |date=2004 |work=Analytical Chemistry |publisher=American Chemical Society ] 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". cite web|url=http://pubs.acs.org/journals/ancham/promo/75th/seminal.html |title=10 Seminal Papers |accessdate=2007-03-30 |date=2004 |work=Analytical Chemistry |publisher=American Chemical Society ] Savitzky and Golay's original paper contained several typographical errors that were subsequently corrected by Steinier, Termonia, and Deltour. [ Jean Steinier, Yves Termonia, Jules Deltour (1972). "Comments on smoothing and differentiation of data by simplified least square procedure". Analytical Chemistry, 44(11): 1906–1909. doi|10.1021/ac60319a045]
Numerical smoothing and differentiation
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