Smoothing removes short-term variations, or "noise" to reveal the important underlying unadulterated form of the data.
Igor´s Smooth operation performs box, "binomial", and Savitzky-Golay smoothing. The different smoothing algorithms convolve the input data with different coefficients.
Smoothing is a kind of low-pass filter. The type of smoothing and the amount of smoothing alters the filter´s frequency response:
Another term for this kind of smoothing is "sliding average", "box smoothing", or "boxcar smoothing". It can be implemented by convolving the input data with a box-shaped pulse of 2*M+1 values all equal to 1/(2*M+1). We call these values the "coefficients" of the "smoothing kernel":
Binomial smoothing is a Gaussian filter. It convolves your data with normalized coefficients derived from Pascal´s triangle at a level equal to the Smoothing parameter. The algorithm is derived from an article by Marchand and Marmet (1983).
Savitzky-Golay smoothing uses a different set of precomputed coefficients popular in the field of chemistry. It is a type of Least Squares Polynomial smoothing. The amount of smoothing is controlled by two parameters: the polynomial order and the number of points used to compute each smoothed output value.
- Marchand, P., and L. Marmet, Binomial smoothing filter: A way to avoid some pitfalls of least square polynomial smoothing, Rev. Sci. Instrum., 54, 1034-41, 1983.
- Savitzky, A., and M.J.E. Golay, Smoothing and differentiation of data by simplified least squares procedures, Analytical Chemistry, 36, 1627-1639, 1964.