About: Savitzky–Golay filter

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A Savitzky–Golay filter is a digital filter that can be applied to a set of digital data points for the purpose of smoothing the data, that is, to increase the precision of the data without distorting the signal tendency. This is achieved, in a process known as convolution, by fitting successive sub-sets of adjacent data points with a low-degree polynomial by the method of linear least squares. When the data points are equally spaced, an analytical solution to the least-squares equations can be found, in the form of a single set of "convolution coefficients" that can be applied to all data sub-sets, to give estimates of the smoothed signal, (or derivatives of the smoothed signal) at the central point of each sub-set. The method, based on established mathematical procedures, was popularized

Attributes	Values
rdf:type	software
rdfs:label	Savitzky-Golay-Filter (de) Filtro de Savitzky–Golay (es) Algorithme de Savitzky-Golay (fr) Savitzky-Golayfilter (nl) Savitzky–Golay filter (en)
rdfs:comment	L'algorithme de Savitzky-Golay est une méthode utilisée en traitement du signal pour lisser une courbe et en extraire les dérivées successives. Il a été décrit en 1964 par (en) et Marcel Golay. (fr) Een Savitzky-Golayfilter is een wiskundig filter uit de signaalverwerking voor toepassing op equidistante getalsmatige data. De methode is gebaseerd op bestaande wiskundige technieken en werd voor het eerst in 1964 beschreven door en . Het filter maakt het oorspronkelijke signaal "gladder", dat wil zeggen vlakt snelle wisselingen af, waardoor ruis wordt uitgefilterd. Tevens kan het filter gebruikt worden om van het gefilterde signaal afgeleiden te bepalen. De afvlakking gebeurt door in het midden van een venster de gefilterde waarde te bepalen als gewogen som van de oorspronkelijke data in het venster. De wegingsfactoren worden bepaald met een polynoom die in een omgeving van het punt goed bij de data past. (nl) Das Savitzky-Golay-Filter ist ein mathematisches in der Signalverarbeitung. Es wurde erstmals 1964 von und Marcel J. E. Golay beschrieben. Es leistet im Wesentlichen eine polynomiale Regression (k-ten Grades) über einer Serie von Werten auf wenigstens k+1 äquidistanten Stützstellen, um einen geglätteten Wert für jeden Punkt zu bestimmen. Ein Vorteil des Savitzky-Golay-Filters gegenüber anderen ist, dass Anteile von hohen Frequenzen nicht einfach abgeschnitten werden, sondern in die Berechnung mit einfließen. Dadurch zeigt das Filter ausgezeichnete Eigenschaften der Verteilung wie relative Maxima, Minima und Streuung zu erhalten, die von herkömmlichen Methoden wie der Bildung des gleitenden Mittelwerts gewöhnlich durch Abflachung oder Verschiebung verfälscht werden. (de) El filtro de Savitzky–Golay es un tipo de filtro, descrito por primera vez en 1964 por y . El método Savitzky–Golay se basa en el cálculo de una regresión polinomial local (de grado k), con al menos k+1 puntos equiespaciados, para determinar el nuevo valor de cada punto. El resultado será una función similar a los datos de entrada, pero suavizada. Se describen métodos para calcular desde la primera a la quinta derivada. (es) A Savitzky–Golay filter is a digital filter that can be applied to a set of digital data points for the purpose of smoothing the data, that is, to increase the precision of the data without distorting the signal tendency. This is achieved, in a process known as convolution, by fitting successive sub-sets of adjacent data points with a low-degree polynomial by the method of linear least squares. When the data points are equally spaced, an analytical solution to the least-squares equations can be found, in the form of a single set of "convolution coefficients" that can be applied to all data sub-sets, to give estimates of the smoothed signal, (or derivatives of the smoothed signal) at the central point of each sub-set. The method, based on established mathematical procedures, was popularized (en)
foaf:depiction
dcterms:subject	Filter theory Signal estimation
Wikipage page ID	1988157 (xsd:integer)
Wikipage revision ID	1124050452 (xsd:integer)
Link from a Wikipage to another Wikipage	Moving average Real-valued function Normal equations Degree (angle) Variance Vector space Interpolation Standard deviation Convolution Correlation Cramer's rule Analytical Chemistry (journal) Analytical chemistry Matrix (mathematics) Maxima and minima Function (mathematics) GNU MPFR GNU Multiple Precision Arithmetic Library Equivalence point Objective function Low-pass filter dbr:Malonic_acid Sinc function Statistics Faulhaber's formula Full width at half maximum Identity matrix Kernel smoother Smoothing spline Spline (mathematics) Stencil (numerical analysis) Linear least squares (mathematics) Cauchy distribution Window function Local regression Filter theory Signal estimation Fourier transform Bandwidth (signal processing) Normal distribution Pascal (programming language) Diagonal matrix Digital filter Marcel J. E. Golay Recursion Stopband Abraham Savitzky Absorption band Codomain Digital data Discrete Fourier transform Polynomial Inflection point Open-source software Orthogonal polynomials Rational number Signal-to-noise ratio Smoothing Vandermonde matrix Titration curve Numerical differentiation Variance-covariance matrix Analytical solution Gram polynomial Chemical analysis Error propagation dbr:Doi:10.5281/zenodo.1257898 dbr:Doi:10.5281/zenodo.835283 dbr:Whittaker–Henderson_smoothing
Link from a Wikipage to an external page	http://www.statistics4u.info/fundstat_eng/cc_filter_savgolay.html https://books.google.com/books%3Fid=fRcvAQAAIAAJ%7Ctitle=Data https://doi.org/10.5281/zenodo.835283 https://sites.google.com/site/chandraacads/ https://sites.google.com/site/chandraacads/resources/sg-filter/db

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