Optimum window length of Savitzky-Golay filters with arbitrary order

TL;DR

This paper derives an optimal window length for Savitzky-Golay filters of any order to minimize mean square error, introducing an improved algorithm for its determination based on Chebyshev polynomials.

Contribution

It presents a novel algorithm to determine the optimal window length for Savitzky-Golay filters of arbitrary order, enhancing existing methods.

Findings

The proposed algorithm outperforms existing methods in selecting window length.

Optimal window length reduces mean square error in denoising tasks.

The method is applicable to various domains using Savitzky-Golay filters.

Abstract

One of the widely used denoising methods in different domains is the Savitzky-Golay (SG) filter. The SG filter has two design parameters: window length and the filter order. As the length of the window increases, the estimation variance decreases, but the bias error increases at the same time. Mean square error (MSE) measure includes both bias and variance criteria. In this paper, we obtain the optimal window length of an SG filter with arbitrary order which minimizes the MSE. To achieve the optimal window length, we propose an algorithm whose performance is better than the existing methods. In this paper, we follow the viewpoint proposed by Persson and Strang and design the filter on the basis of Chebyshev orthogonal polynomials