arXiv subjects

Paul W. Oxby

Publications and source records attributed to Paul W. Oxby.

3 recordsLinked to original sources

arXiv2024

Confidence Intervals for the Savitzky-Golay Filter with an Application to the Keeling Data for Atmospheric CO2

The Savitzky-Golay FIR digital filter is based on a least-squares polynomial fit to a sample of equally spaced data. The polynomial fit gives the filter the ability to preserve moments of features in the data like peak width. However the S-G filter is not generally regarded as having a sound statistical basis. This puts the filter in the category of smoothing filters where the degree of smoothing depends on the somewhat arbitrary choice of the filter parameters. This arbitrariness makes the variance of the residuals between the filter input and output an unreliable estimate of the variance of the noise in the filter input. And without a reliable estimate of the input noise variance there is no basis for determining statistically meaningful confidence intervals on the filter output. This paper proposes a method of using the S-G filter to determine a reliable estimate of the variance of the noise in the data. This estimate is then used as the basis for selecting appropriate filter parameters and determining statistically meaningful confidence intervals on the filter output. To illustrate the proposed method an analysis of the Keeling measurements of atmospheric CO2 concentration is presented.

eess.SP↗

arXiv2024

A Function Based on Chebyshev Polynomials as an Alternative to the Sinc Function in FIR Filter Design

The sinc function is often used as the basis for the design of discrete linear-phase FIR filters. However the Fourier transform of the truncated sinc function exhibits ripple in the pass band due to the Gibbs phenomenon. This paper introduces an alternative function based on Chebyshev polynomials whose Fourier transform decreases monotonically in the pass band. Furthermore this function features an intrinsic window function with an adjustable parameter influencing the Fourier transform in the transition and stop bands.

eess.SP↗

arXiv2021

An Optimal Weighting Function for the Savitzky-Golay Filter

The Savitzky-Golay FIR digital filter is based on a least-squares polynomial fit to a hypothetical sample of equally spaced data. This gives the filter the ability to preserve moments of features like peaks in the input. Descriptions of the filter typically consider the case where equal weights are implicitly applied to the residuals of the fit. In a largely overlooked paper Turton showed that weighting the residuals with a triangular function significantly improves the frequency response of the filter in the stopband. The Savitzky-Golay filter is commonly referred to as a smoothing filter. This paper uses a particular measure of smoothness to show that a quadratic residual weighting function optimizes the smoothness of the filter output for a given sample size and degree of the fitting polynomial. This weighting function can provide substantially better smoothness than that with a constant weighting function.

eess.SP↗