The Gibbs Phenomenon for L1loc Kernels
โ Scribed by L. De Michele; D. Roux
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 131 KB
- Volume
- 100
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
When a Fourier series is used to approximate a function with a jump discontinuity, an overshoot at the discontinuity occurs. This phenomenon was noticed by Michelson [6] and explained by Gibbs [3] in 1899. This phenomenon is known as the Gibbs effect. In this paper, possible Gibbs effects will be lo
It is shown that a Gibbs phenomenon occurs in the wavelet expansion of a function with a jump discontinuity at 0 for a wide class of wavelets. Additional results are provided on the asymptotic behavior of the Gibbs splines and on methods to remove the Gibbs phenomenon.