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- Title
Numerical Generation of Images for the Gibbs Phenomenon Near a Corner in the Plane.
- Authors
Khurram, Alia; Kammler, David W.
- Abstract
In this paper we have studied the Gibbs ripples associated with an α-corner, i.e., the indicator function for the smaller region of ℝ² bounded by two rays from the origin that intersect at the angle α, 0 < α < π. (Such corners cannot occur in the univariate case.) We have done this by removing from the Fourier representation all components that lie outside of a disk with radius σ ≥ 0. We have used a technique to rearrange the approximating integrals in a form that facilitates efficient computation. We then produced two dimensional images for the Gibbs ripples that correspond to the corner angles α = π/3, π/2, 2π/3, π. We observed that the maximum overshoot occurs near the corner.
- Subjects
NUMERICAL analysis; IMAGE analysis; GIBBS phenomenon; PLANE geometry; MATHEMATICAL bounds; FOURIER transforms
- Publication
IAENG International Journal of Applied Mathematics, 2014, Vol 44, Issue 1, p15
- ISSN
1992-9978
- Publication type
Article