Savitzky–Golay smoothing filter
Encyclopedia
The Savitzky–Golay smoothing filter is a type of filter
first described in 1964 by Abraham Savitzky
and Marcel J. E. Golay
.
The Savitzky–Golay method essentially performs a local polynomial regression
(of degree k) on a series of values (of at least k+1 points which are treated as being equally spaced in the series) to determine the smoothed
value for each point. Methods are also provided for calculating the first up to the fifth derivative
s. A modern implementation is given in ref.
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
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".
Savitzky and Golay's original paper contained several typographical errors that were subsequently corrected by Steinier, Termonia, and Deltour.
Filter (signal processing)
In signal processing, a filter is a device or process that removes from a signal some unwanted component or feature. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal...
first described in 1964 by Abraham Savitzky
Abraham Savitzky
Abraham Savitzky 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. Golay an oft-cited paper describing the Savitzky-Golay Smoothing...
and Marcel J. E. Golay
Marcel J. E. Golay
Marcel J.E. Golay 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.-Career:...
.
The Savitzky–Golay method essentially performs a local polynomial regression
Polynomial regression
In statistics, polynomial regression is a form of linear regression in which the relationship between the independent variable x and the dependent variable y is modeled as an nth order polynomial...
(of degree k) on a series of values (of at least k+1 points which are treated as being equally spaced in the series) to determine the smoothed
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 algorithms are used in smoothing...
value for each point. Methods are also provided for calculating the first up to the fifth derivative
Derivative
In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...
s. A modern implementation is given in ref.
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
Analytical Chemistry (journal)
Analytical Chemistry is a peer-reviewed scientific journal, published since 1929 by the American Chemical Society. It is currently indexed/abstracted in: Chemical Abstracts Service, CABI, EBSCOhost, ProQuest, PubMed, Scopus, and Web of Science...
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".
Savitzky and Golay's original paper contained several typographical errors that were subsequently corrected by Steinier, Termonia, and Deltour.