Savgol: Difference between revisions
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===Synopsis=== | ===Synopsis=== | ||
:[y_hat, | :[y_hat, D] = savgol(y,''width,order,deriv,options'') | ||
===Description=== | ===Description=== | ||
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SAVGOL performs Savitzky-Golay smoothing on a matrix of row vectors y. At each increment (column) a polynomial of order ''order'' is fitted to the number of points ''width'' surrounding the increment. An estimate for the value of the function (''deriv = 0'') or derivative of the function (''deriv > 0'') at the increment is calulated from the fit resulting in a smoothed function y_hat. E.g. see A. Savitzky and M.J.E. Golay, Anal. Chem. '''36''', 1627 (1964). | SAVGOL performs Savitzky-Golay smoothing on a matrix of row vectors y. At each increment (column) a polynomial of order ''order'' is fitted to the number of points ''width'' surrounding the increment. An estimate for the value of the function (''deriv = 0'') or derivative of the function (''deriv > 0'') at the increment is calulated from the fit resulting in a smoothed function y_hat. E.g. see A. Savitzky and M.J.E. Golay, Anal. Chem. '''36''', 1627 (1964). | ||
<tt>[y_hat, | <tt>[y_hat, D] = savgol(y,width,order,deriv)</tt> allows the user to select the number of points in the filter (width, default = 15), the order of the polynomial to fit to the points (order, default = 2), and the order of the derivative (deriv, default = 0). | ||
Output, <tt> | Output, <tt>D</tt>, allows the user to apply smoothing to additional matrices of the same size as y, ''e.g.'' <tt>y_hat2 = y2*D</tt> where y2 is the same size as y used to determine D. | ||
Note: width must be >= 3 and odd, and and deriv must be <= order. | Note: width must be >= 3 and odd, and and deriv must be <= order. | ||
(For more information see: https://eigenvector.com/wp-content/uploads/2020/01/SavitzkyGolay.pdf) | |||
===Options=== | ===Options=== | ||
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: '1/d' weights by the inverse distance from the window center, or | : '1/d' weights by the inverse distance from the window center, or | ||
: a 1 by width vector with values 0<wt<=1 allows for custom weighting. | : a 1 by width vector with values 0<wt<=1 allows for custom weighting. | ||
* '''mode''': [ 1 | {2} ] Use rows or columns. | |||
===Examples=== | ===Examples=== | ||
Latest revision as of 06:32, 18 March 2021
Purpose
Savitzky-Golay smoothing and differentiation.
Synopsis
- [y_hat, D] = savgol(y,width,order,deriv,options)
Description
SAVGOL performs Savitzky-Golay smoothing on a matrix of row vectors y. At each increment (column) a polynomial of order order is fitted to the number of points width surrounding the increment. An estimate for the value of the function (deriv = 0) or derivative of the function (deriv > 0) at the increment is calulated from the fit resulting in a smoothed function y_hat. E.g. see A. Savitzky and M.J.E. Golay, Anal. Chem. 36, 1627 (1964).
[y_hat, D] = savgol(y,width,order,deriv) allows the user to select the number of points in the filter (width, default = 15), the order of the polynomial to fit to the points (order, default = 2), and the order of the derivative (deriv, default = 0).
Output, D, allows the user to apply smoothing to additional matrices of the same size as y, e.g. y_hat2 = y2*D where y2 is the same size as y used to determine D.
Note: width must be >= 3 and odd, and and deriv must be <= order.
(For more information see: https://eigenvector.com/wp-content/uploads/2020/01/SavitzkyGolay.pdf)
Options
options = a structure array with the following fields:
- useexcluded: [ {'true'} | 'false' ], governs how excluded data is handled by the algorithm.
- If 'true', excluded data is used when handling data on the edges of the excluded region (unusual excluded data may influence nearby non-excluded points).
- When 'false', excluded data is never used and edges of excluded regions are handled like edges of the spectrum (may introduce edge artifacts for some derivatives).
- tails: ['traditional' | {'polyinterp'} | 'weighted'], governs how edges of data and excluded regions are handled.
- 'traditional' is an older approach and isn't recommended.
- 'polyinterp' and 'weighted' provide smoother edge transitions.
- 'weighted' uses '1/d' window weighting. It is less affected by end-effects than 'traditional' and 'polyinterp'.
- wt: [ {' '} | '1/d' | [1xwidth] ] allows for weighted least-squares when fitting the polynomials.
- ' ' (empty) provides usual (unweighted) least-squares.
- '1/d' weights by the inverse distance from the window center, or
- a 1 by width vector with values 0<wt<=1 allows for custom weighting.
- mode: [ 1 | {2} ] Use rows or columns.
Examples
If y is 3 by 100 then
y_hat = savgol(y,11,4,2);
yields a 3 by 100 matrix y_hat that contains row vectors of the second derivative of rows of y resulting from an 11-point quartic Savitzky-Golay smooth of each row of y.
See Also
baseline, baselinew, deresolv, line_filter, mscorr, polyinterp, savgolcv, stdfir, testrobustness, wlsbaseline