Detecting discontinuity points from spectral data with the quotient-difference (qd) algorithm
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- 作者：Hassane Allouche ; allouche_hassane@yahoo.fr ; Noura Ghanou ; Khalid Tigma
- 关键词：Location of discontinuity points ; Edge detection ; Fourier series ; Piecewise smooth function ; Gibbs phenomenon ; Qd-algorithm
- 刊名：Journal of Computational and Applied Mathematics
- 出版年：2012
- 出版时间：March, 2012
- 年：2012
- 卷：236
- 期：9
- 页码：2406-2424
- 全文大小：967 K
文摘
This paper introduces a new technique for the localization of discontinuity points from spectral data. Through this work, we will be able to detect discontinuity points of a -periodic piecewise smooth function from its Fourier coefficients. This could be useful in detecting edges and reducing the effects of the Gibbs phenomenon which appears near discontinuities and affects signal restitution. Our approach consists in moving from a discontinuity point detection problem to a pole detection problem, then adapting the quotient-difference (qd) algorithm in order to detect those discontinuity points.