Detecting discontinuity points from spectral data with the quotient-difference (qd) algorithm

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 2π-periodic piecewise smooth function from its Fourier coefficients. This could be useful in detecting edges and reducing the...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 236; no. 9; pp. 2406 - 2424
Main Authors: Allouche, Hassane, Ghanou, Noura, Tigma, Khalid
Format: Journal Article
Language:English
Published: Elsevier B.V 01.03.2012
Subjects:
Edge detection
Fourier series
Gibbs phenomenon
Location of discontinuity points
Piecewise smooth function
Qd-algorithm
Piecewise smooth function
Qd-algorithm
Location of discontinuity points
Gibbs phenomenon
Fourier series
Edge detection
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary: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 2π-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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2011.11.027