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Table of Contents Bivariate Data Smoothing Savitzky-Golay Filter | |
See also: mathematical details, coefficients |
One approach for smoothing the time series is to replace each value of the series with a new value which is obtained from a polynomial fit to 2n+1 neighboring points (including the point to be smoothed), with n being equal to, or greater than the order of the polynomial.
Example: smoothing a time series by using a 2nd order polynomial and 7 data points. The equation for this particular Savitzky-Golay smoothing is defined as follows:
y_{t} = (-2x_{t-3 }+ 3x_{t-2} + 6x_{t-1} + 7x_{t} + 6x_{t+1} + 3x_{t+2} - 2x_{t+3})/21.
The figure below shows the smoothing results (lower trace) for a spiked,
noisy sine signal (upper trace), using a second order polynomial fit with
25 data points. In order to experiment with different smoothing methods,
click at the image below.
Last Update: 2006-Jän-17