The Gibbs' phenomenon

Fay, Temple H.; Kloppers, P. Hendrik

doi:10.1080/00207390117151

Cited by 17 publications

(3 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, there is the interesting Gibbs phenomenon that occurs at jump discontinuities, which is easy to display, straightforward to calculate, and provides the motivation for convergence discussions. This has been the thrust of the recent articles [2,3] appearing in this journal.…”

Section: Introductionmentioning

confidence: 96%

The Gibbs phenomenon for series of orthogonal polynomials

Fay

Kloppers

2006

International Journal of Mathematical Education in Science and

View full text Add to dashboard Cite

This note considers the four classes of orthogonal polynomials -Chebyshev, Hermite, Laguerre, Legendre -and investigates the Gibbs phenomenon at a jump discontinuity for the corresponding orthogonal polynomial series expansions. The perhaps unexpected thing is that the Gibbs constant that arises for each class of polynomials appears to be the same as that for Fourier series expansions. Each class of polynomials has features which are interesting numerically. Finally a plausibility argument is included showing that this phenomenon for the Gibbs constants should not have been unexpected. These findings suggest further investigations suitable for undergraduate research projects or small group investigations.

show abstract

Section: Introductionmentioning

confidence: 96%

The Gibbs phenomenon for series of orthogonal polynomials

Fay

Kloppers

2006

International Journal of Mathematical Education in Science and

View full text Add to dashboard Cite

show abstract

“…A caveat of PPG sensors is their tendency to saturate, which does not provide meaningful clinical information [ 12 , 13 ]. On top of this, when applying common biosignal filtering techniques, saturated portions lead to distorted filtered signal, a ringing effect, which in turn contributes to inaccurate peak detection and extracted features [ 12 , 14 , 15 , 16 ]. Consequently, alternative measurement sites need to be explored and validated to ensure that high-quality signals can be obtained.…”

Section: Introductionmentioning

confidence: 99%

Benchmarking of Sensor Configurations and Measurement Sites for Out-of-the-Lab Photoplethysmography

Supelnic,

Ferreira,

Bota

et al. 2023

Sensors

View full text Add to dashboard Cite

Photoplethysmography (PPG) is used for heart-rate monitoring in a variety of contexts and applications due to its versatility and simplicity. These applications, namely studies involving PPG data acquisition during day-to-day activities, require reliable and continuous measurements, which are often performed at the index finger or wrist. However, some PPG sensors are susceptible to saturation, motion artifacts, and discomfort upon their use. In this paper, an off-the-shelf PPG sensor was benchmarked and modified to improve signal saturation. Moreover, this paper explores the feasibility of using an optimized sensor in the lower limb as an alternative measurement site. Data were collected from 28 subjects with ages ranging from 18 to 59 years. To validate the sensors’ performance, signal saturation and quality, wave morphology, performance of automatic systolic peak detection, and heart-rate estimation, were compared. For the upper and lower limb locations, the index finger and the first toe were used as reference locations, respectively. Lowering the amplification stage of the PPG sensor resulted in a significant reduction in signal saturation, from 18% to 0.5%. Systolic peak detection at rest using an automatic algorithm showed a sensitivity and precision of 0.99 each. The posterior wrist and upper arm showed pulse wave morphology correlations of 0.93 and 0.92, respectively. For these locations, peak detection sensitivity and precision were 0.95, 0.94 and 0.89, 0.89, respectively. Overall, the adjusted PPG sensors are a good alternative for obtaining high-quality signals at the fingertips, and for new measurement sites, the posterior pulse and the upper arm allow for high-quality signal extraction.

show abstract

“…When the signals are modulated by a carrier square wave of unit amplitude, as may occur in fast digitization of modulated signals [5], two considerations may come into play. First, of course, Gibbs' phenomenon [2]. Second, the realization that the operations on the original signal correspond to the integration of a continuous function f over a domain where the support of f is periodically reduced by a factor of 1/2.…”

Section: Introductionmentioning

confidence: 99%