savgol

C++ implementation of Savitzky Golay Filter based on the original paper : "Smoothing and Differentiation of Data by Simplified Least Squares Procedures" by A.Savitzky and M. J.E Golay". [1]

• The implementation is close to the original publication with corrections taken from [2] . The convolution weights for each given window size are stored in a constexpr map.

• there is no padding implemented so far. The data points at the bounds left unchanged.

usage

#include <vector>
#include "savgol.hpp"

std::vector<float> data{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};

std::vector<double> filtered_data;

filter::savgol(data.begin(), data.end(), sd::back_inserter(filtered_data),filter::SmoothQuadCubic(5) );

implementation

available Convolution Operators

SmoothQuadCubic :

SmoothQuarticQuintic :

DeriveQuadFirst :

---

SmoothGaussian: to make comparisions to SG filter, the gaussian kernel is approximated by binominal coefficients, taken from Pascals triangle.

SmoothAverage: to make comparisions to SG filter, convolution weights are constant =1.

available window sizes

• as presentented in the original paper the window sizes are odd numbers, up to a size of 25

Demonstration

[1] A. Savitzky, M. J. E. Golay: Smoothing and Differentiation of Data by Simplified Least Squares Procedures. In: Analytical Chemistry. Volume 36, No. 8, June 1964, p. 1627–1639, doi:10.1021/ac60214a047.

[2] J. Steiner, Y. Termonia, J. Deltour: Comments on Smoothing And Differentiation Of Data By Simplified Least Square Procedure In: Analytical Chemistry. Volume 44, No. 11, 1. Sept 1972, p. 1906–1909