A nonlinear generalization of the Savitzky-Golay filter and the quantitative analysis of saccades

Weiwei Dai, Ivan Selesnick, John Ross Rizzo, Janet Rucker, Todd Hudson

Research output: Contribution to journalArticle

Abstract

The Savitzky-Golay (SG) filter is widely used to smooth and differentiate time series, especially biomedical data. However, time series that exhibit abrupt departures from their typical trends, such as sharp waves or steps, which are of physiological interest, tend to be oversmoothed by the SG filter. Hence, the SG filter tends to systematically underestimate physiological parameters in certain situations. This article proposes a generalization of the SG filter to more accurately track abrupt deviations in time series, leading to more accurate parameter estimates (e.g., peak velocity of saccadic eye movements). The proposed filtering methodology models a time series as the sum of two component time series: a low-frequency time series for which the conventional SG filter is well suited, and a second time series that exhibits instantaneous deviations (e.g., sharp waves, steps, or more generally, discontinuities in a higher order derivative). The generalized SG filter is then applied to the quantitative analysis of saccadic eye movements. It is demonstrated that (a) the conventional SG filter underestimates the peak velocity of saccades, especially those of small amplitude, and (b) the generalized SG filter estimates peak saccadic velocity more accurately than the conventional filter.

Original languageEnglish (US)
Article number10
JournalJournal of vision
Volume17
Issue number9
DOIs
StatePublished - 2017

Fingerprint

Saccades

Keywords

  • Differentiation
  • Quantitative saccade analysis
  • Saccade peak velocity
  • Savitzky-Golay filter
  • Smoothing
  • Sparsity

ASJC Scopus subject areas

  • Ophthalmology
  • Sensory Systems

Cite this

A nonlinear generalization of the Savitzky-Golay filter and the quantitative analysis of saccades. / Dai, Weiwei; Selesnick, Ivan; Rizzo, John Ross; Rucker, Janet; Hudson, Todd.

In: Journal of vision, Vol. 17, No. 9, 10, 2017.

Research output: Contribution to journalArticle

Dai, Weiwei ; Selesnick, Ivan ; Rizzo, John Ross ; Rucker, Janet ; Hudson, Todd. / A nonlinear generalization of the Savitzky-Golay filter and the quantitative analysis of saccades. In: Journal of vision. 2017 ; Vol. 17, No. 9.
@article{4a8b4d26884b4d26a80f377d98ff5b3b,
title = "A nonlinear generalization of the Savitzky-Golay filter and the quantitative analysis of saccades",
abstract = "The Savitzky-Golay (SG) filter is widely used to smooth and differentiate time series, especially biomedical data. However, time series that exhibit abrupt departures from their typical trends, such as sharp waves or steps, which are of physiological interest, tend to be oversmoothed by the SG filter. Hence, the SG filter tends to systematically underestimate physiological parameters in certain situations. This article proposes a generalization of the SG filter to more accurately track abrupt deviations in time series, leading to more accurate parameter estimates (e.g., peak velocity of saccadic eye movements). The proposed filtering methodology models a time series as the sum of two component time series: a low-frequency time series for which the conventional SG filter is well suited, and a second time series that exhibits instantaneous deviations (e.g., sharp waves, steps, or more generally, discontinuities in a higher order derivative). The generalized SG filter is then applied to the quantitative analysis of saccadic eye movements. It is demonstrated that (a) the conventional SG filter underestimates the peak velocity of saccades, especially those of small amplitude, and (b) the generalized SG filter estimates peak saccadic velocity more accurately than the conventional filter.",
keywords = "Differentiation, Quantitative saccade analysis, Saccade peak velocity, Savitzky-Golay filter, Smoothing, Sparsity",
author = "Weiwei Dai and Ivan Selesnick and Rizzo, {John Ross} and Janet Rucker and Todd Hudson",
year = "2017",
doi = "10.1167/17.9.10",
language = "English (US)",
volume = "17",
journal = "Journal of vision",
issn = "1534-7362",
number = "9",

}

TY - JOUR

T1 - A nonlinear generalization of the Savitzky-Golay filter and the quantitative analysis of saccades

AU - Dai, Weiwei

AU - Selesnick, Ivan

AU - Rizzo, John Ross

AU - Rucker, Janet

AU - Hudson, Todd

PY - 2017

Y1 - 2017

N2 - The Savitzky-Golay (SG) filter is widely used to smooth and differentiate time series, especially biomedical data. However, time series that exhibit abrupt departures from their typical trends, such as sharp waves or steps, which are of physiological interest, tend to be oversmoothed by the SG filter. Hence, the SG filter tends to systematically underestimate physiological parameters in certain situations. This article proposes a generalization of the SG filter to more accurately track abrupt deviations in time series, leading to more accurate parameter estimates (e.g., peak velocity of saccadic eye movements). The proposed filtering methodology models a time series as the sum of two component time series: a low-frequency time series for which the conventional SG filter is well suited, and a second time series that exhibits instantaneous deviations (e.g., sharp waves, steps, or more generally, discontinuities in a higher order derivative). The generalized SG filter is then applied to the quantitative analysis of saccadic eye movements. It is demonstrated that (a) the conventional SG filter underestimates the peak velocity of saccades, especially those of small amplitude, and (b) the generalized SG filter estimates peak saccadic velocity more accurately than the conventional filter.

AB - The Savitzky-Golay (SG) filter is widely used to smooth and differentiate time series, especially biomedical data. However, time series that exhibit abrupt departures from their typical trends, such as sharp waves or steps, which are of physiological interest, tend to be oversmoothed by the SG filter. Hence, the SG filter tends to systematically underestimate physiological parameters in certain situations. This article proposes a generalization of the SG filter to more accurately track abrupt deviations in time series, leading to more accurate parameter estimates (e.g., peak velocity of saccadic eye movements). The proposed filtering methodology models a time series as the sum of two component time series: a low-frequency time series for which the conventional SG filter is well suited, and a second time series that exhibits instantaneous deviations (e.g., sharp waves, steps, or more generally, discontinuities in a higher order derivative). The generalized SG filter is then applied to the quantitative analysis of saccadic eye movements. It is demonstrated that (a) the conventional SG filter underestimates the peak velocity of saccades, especially those of small amplitude, and (b) the generalized SG filter estimates peak saccadic velocity more accurately than the conventional filter.

KW - Differentiation

KW - Quantitative saccade analysis

KW - Saccade peak velocity

KW - Savitzky-Golay filter

KW - Smoothing

KW - Sparsity

UR - http://www.scopus.com/inward/record.url?scp=85027691619&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85027691619&partnerID=8YFLogxK

U2 - 10.1167/17.9.10

DO - 10.1167/17.9.10

M3 - Article

VL - 17

JO - Journal of vision

JF - Journal of vision

SN - 1534-7362

IS - 9

M1 - 10

ER -