Savitzky-Golay Filter in C++

Author: Lekan Ogunmolu

Table of Contents

• Introduction
• Dependencies
• Usage
• Compilation
• Citation
• Issues
• Changelog

Introduction

Nicely computes the Vandermonde matrix, Savitzky-Golay differentiation filters, and smoothing coefficients for any sequential signal. It is a textbook implementation of the Savitzky-Golay Filter. Initial testing of this code was on a Ubuntu 14.04.02 Trusty OS running Linux 4.4 but will work on any other Linux/Windows/Mac OS machine with little effort.

Below are examples of how the filter smoothes out a noisy depth map data from the kinect time-of-flight sensor:

Dependencies

• Eigen3 Library for the linear algebra of the matrices, vectors and related algorithms. You can download the 3.2.5 library which I used from here and follow the README instructions after unpacking the tarball to install.

Usage

• ./savgol

  Options

  • -h or --help: print out the help menu.

  • Example: Compute the savitzky-golay filter coefficients with frame size, F = 5 and polynomial order 3 (these are the default parameters of the filter) for linearly spaced data points between x_min = 900 and x_max = 980. A typical cmd line usage:

    ./savgoal 9 5 where F = 9 and k = 5.

  • To pass in your arbitrary data points between a value x_min and x_max, run this way in order: ./savgoal F k x_min x_max.

  The filtered values are returned to the console. Note that the Frame size should ideally be odd.

Components

• MatrixXi vander(const int F);

  • Computes the Vandermonde matrix and the polynomial of basis vectors; it flips the vector column-wise, left to right.

• MatrixXf B = MatrixXf sgdiff(int k, double F)

  • Designs a Savitzky-Golay FIR smoothing filter, B, with polynomial order k and frame size F of convolution coefficients. The polynomial order, k, must be less than the frame size F, and F must be odd.

• savgolfilt(x, x_on, k, F)

  • Computes the smoothed values of the signal x, whose tansient on is x_on initialized with size F.

• Note In calculating the transient off, x_off will be the last (F-1) x values, where x's are the data sequence we want to filter.If you are smoothing data offline, then this code will work seamlessly. Just load your data in the main() function where, for an example, I have used linearly spaced values between 900 and 980 at a frame 5 size for my steady state values.

Note, if you are smoothing data in real time, you need to find a way to let your compiler pick the last F-length samples from your data in order to compute your transient off, i.e., x_off. You could have the program wait for x_milliseconds after stopping your code before you pick the transient off, for example.

Compilation

There is a CMakeLists.txt file in the project root folder. From the project root directory:

1. Create a build directory: mkdir build && cd build
2. Compile the cpp code: cmake ../
3. Build your executable: make
4. Run the executable: ./savgol

Citation

If you have used Savitzky-Golay in your work, please cite it.

@misc{Savitzky-Golay,
  author = {Ogunmolu, Olalekan},
  title = {{Savitzky-Golay Filter in C++}},
  year = {2015},
  howpublished = {\url{https://github.com/lakehanne/Savitzky-Golay}},
  note = {Accessed August 15, 2015}
}

Issues

If you have issues running the files, please use the issues tab to open a bug. I will generally respond within a 24-hour period.

Changelog

• Added citation to README (August 14, 2015)
• Added examples to int main() function (August 15, 2015)
• Modified frame size and polynomial order to be reconfigurable at run time (July 1, 2016)

TODO

Add a plotter to plot the filtered values on a gtk chart?

Reference

INTRODUCTION TO SIGNAL PROCESSING

Sophocles J. Orfanidis, Prentice Hall, 2010

Chapter 8; Section 8.3.5