Savitzky–Golay smoothing filter
- 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. [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 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"[ 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] ]See also Numerical smoothing and differentiation
References
Wikimedia Foundation.
2010.
Look at other dictionaries:
Smoothing — In statistics and image processing, to smooth a data set is to create an approximating function that attempts to capture important patterns in the data, while leaving out noise or other fine scale structures/rapid phenomena. Many different… … Wikipedia
Golay — Cette page d’homonymie répertorie les différents sujets et articles partageant un même nom. Code de Golay, un code correcteur Cellule de Golay (en), un détecteur en spectroscopie infrarouge Filtre électronique de Stavitzky Golay … Wikipédia en Français
Numerical smoothing and differentiation — An experimental datum value can be conceptually described as the sum of a signal and some noise, but in practice the two contributions cannot be separated. The purpose of smoothing is to increase the Signal to noise ratio without greatly… … Wikipedia
Marcel J. E. Golay — (* 3. Mai 1902 in Neuchâtel, Schweiz; † 27. April 1989) war ein Schweizer Mathematiker, Physiker und Informatiker, welcher Mathematik auf militärische und industrielle Probleme anwendete. Karriere Golay studierte Elektrotechnik an der… … Deutsch Wikipedia
Marcel J. E. Golay — Marcel J.E. Golay (May 3, 1902 – 1989) was a Swiss born mathematician, physicist, and information theorist, who applied mathematics to real world military and industrial problems. He was born in Neuchâtel, Switzerland. Contents 1 Career 2… … Wikipedia
Abraham Savitzky — (1919 ndash; February 5, 1999) was an American analytical chemist.He specialized in the digital processing of infrared spectra and was awarded seven patents in that field. While employed by Perkin Elmer, Savitzky coauthored with Marcel J. E.… … Wikipedia
List of mathematics articles (S) — NOTOC S S duality S matrix S plane S transform S unit S.O.S. Mathematics SA subgroup Saccheri quadrilateral Sacks spiral Sacred geometry Saddle node bifurcation Saddle point Saddle surface Sadleirian Professor of Pure Mathematics Safe prime Safe… … Wikipedia
OpenChrom — Developer(s) Philip Wenig Stable release 0.5.0 / October 30, 2011; 0 days ago (2011 10 30) Written in Java Operating s … Wikipedia
