Savitzky–Golay filter

A Savitzky–Golay filter is a <a href="/facts/Digital_filter/2wcxCRdh">digital filter</a> that can be applied to a set of <a href="/facts/Digital_data/JChckAvr">digital data</a> points for the purpose of <a href="/facts/Smoothing/2svFjsbI">smoothing</a> the data, that is, to increase the precision of the data without distorting the signal tendency. This is achieved, in a process known as <a href="/facts/Convolution/PVPrdz9J">convolution</a>, by fitting successive sub-sets of adjacent data points with a low-degree <a href="/facts/Polynomial/Lzak8VVx">polynomial</a> by the method of <a href="/facts/Linear_least_squares_(mathematics)/dKctFUCV">linear least squares</a>. When the data points are equally spaced, an <a href="/facts/Analytical_solution/y0xCXlSk">analytical solution</a> 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 by <a href="/facts/Abraham_Savitzky/0IMb5Bpp">Abraham Savitzky</a> and <a href="/facts/Marcel_J._E._Golay/8BJ8gj2T">Marcel J. E. Golay</a>, who published tables of convolution coefficients for various polynomials and sub-set sizes in 1964. Some errors in the tables have been corrected. The method has been extended for the treatment of 2- and 3-dimensional data.
Savitzky and Golay's paper is one of the most widely cited papers in the journal <a href="/facts/Analytical_Chemistry_(journal)/ErEf0JLm">Analytical Chemistry</a> 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–Golay filter open-in-new

Savitzky–Golay filter