Journal of Computational and Applied Mathematics - Orthogonal polynomials and numerical methods
Accurate reconstructions of functions of finite regularity from truncated Fourier series expansions
Mathematics of Computation
On the Gibbs Phenomenon and Its Resolution
SIAM Review
Detection of Edges in Spectral Data II. Nonlinear Enhancement
SIAM Journal on Numerical Analysis
Towards the resolution of the Gibbs phenomena
Journal of Computational and Applied Mathematics
Determining the locations and discontinuities in the derivatives of functions
Applied Numerical Mathematics
Detection of Edges in Spectral Data III--Refinement of the Concentration Method
Journal of Scientific Computing
Iterative methods based on spline approximations to detect discontinuities from Fourier data
Journal of Computational and Applied Mathematics
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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 2@p-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.