Numerical smoothing and differentiation
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High Quality Content by WIKIPEDIA articles! An experimental datum value can be conceptually described as the sum of a signal and some noise, but in practice the two contributions cannot be separated. The purpose of smoothing is to increase the Signal-to-noise ratio without greatly distorting the signal. One way to achieve this is by fitting successive sets of m data points to a polynomial of degree less than m by the method of linear least squares. Once the coefficients of the smoothing polynomial have been calculated they can be used to give estimates of the signal or its derivatives.

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High Quality Content by WIKIPEDIA articles! An experimental datum value can be conceptually described as the sum of a signal and some noise, but in practice the two contributions cannot be separated. The purpose of smoothing is to increase the Signal-to-noise ratio without greatly distorting the signal. One way to achieve this is by fitting successive sets of m data points to a polynomial of degree less than m by the method of linear least squares. Once the coefficients of the smoothing polynomial have been calculated they can be used to give estimates of the signal or its derivatives.