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Since the Gibbs phenomenon comes from undershooting, it may be eliminated by using kernels that are never negative, such as the Fejér kernel. [12] [13]In practice, the difficulties associated with the Gibbs phenomenon can be ameliorated by using a smoother method of Fourier series summation, such as Fejér summation or Riesz summation, or by using sigma-approximation.
Josiah Willard Gibbs Born (1839-02-11) February 11, 1839 New Haven, Connecticut, U.S. Died April 28, 1903 (1903-04-28) (aged 64) New Haven, Connecticut, U.S. Nationality American Alma mater Yale College (BA, PhD) Known for List Statistical mechanics Chemical thermodynamics Chemical potential Cross product Dyadics Exergy Principle of maximum work Phase rule Phase space Physical optics Physics ...
The sinc function, the impulse response for an ideal low-pass filter, illustrating ringing for an impulse. The Gibbs phenomenon, illustrating ringing for a step function.. By definition, ringing occurs when a non-oscillating input yields an oscillating output: formally, when an input signal which is monotonic on an interval has output response which is not monotonic.
The term () is the Lanczos σ factor, which is responsible for eliminating most of the Gibbs phenomenon. This is sampling the right side of the main lobe of the sinc {\displaystyle \operatorname {sinc} } function to rolloff the higher frequency Fourier Series coefficients.
The Marangoni effect (also called the Gibbs–Marangoni effect) is the mass transfer along an interface between two phases due to a gradient of the surface tension. In the case of temperature dependence, this phenomenon may be called thermo-capillary convection [ 1 ] or Bénard–Marangoni convection .
Jerri is a double-awarded Fulbright Scholar at the Sultan Qaboos University in Muscat, Oman(1997), and a second time, at the Yarmouk University in Irbid, Jordan (2001). He is the Founding Executive Editor of Sampling Theory In Signal And Image Processing (STSIP) - An International Journal., [2] and the owner of Sampling Publishing.
A curiosity of the convergence of the Fourier series representation of the square wave is the Gibbs phenomenon. Ringing artifacts in non-ideal square waves can be shown to be related to this phenomenon. The Gibbs phenomenon can be prevented by the use of σ-approximation, which uses the Lanczos sigma factors to help the sequence converge more ...
Henry Wilbraham (25 July 1825 – 13 February 1883) was an English mathematician. He is known for discovering and explaining the Gibbs phenomenon nearly fifty years before J. Willard Gibbs did. Gibbs and Maxime Bôcher, as well as nearly everyone else, were unaware of Wilbraham's paper on the Gibbs phenomenon.