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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| Veröffentlicht in: | Journal of computational and applied mathematics Jg. 236; H. 9; S. 2406 - 2424 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Elsevier B.V
01.03.2012
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| ISSN: | 0377-0427, 1879-1778 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Ghanou, Noura Allouche, Hassane Tigma, Khalid |
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| Cites_doi | 10.1137/S0036142999359153 10.1137/1014001 10.1016/j.apnum.2007.01.018 10.1016/j.cam.2010.04.027 10.1016/0377-0427(92)90260-5 10.1007/BF02149767 10.1007/s10598-007-0010-3 10.1090/S0025-5718-1995-1265014-7 10.1137/S0036144596301390 10.1016/S0377-0427(03)00500-4 10.1007/s10915-007-9170-8 |
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| Keywords | Piecewise smooth function Qd-algorithm Location of discontinuity points Gibbs phenomenon Fourier series Edge detection |
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| References | Beckermann, Carstensen (br000075) 1996; 12 Gelb, Cates (br000010) 2008; 36 Archibald, Gelb, Yoon (br000085) 2008; 58 Rutishauser (br000065) 1957 Gragg (br000055) 1972; 14 Eckhoff (br000015) 1995; 64 Lanczos (br000025) 1996 Eckhoff (br000020) 1995; 64 Krylov, Najafi (br000090) 2007; 18 Gelb, Tadmor (br000005) 2000; 38 Henrici (br000060) 1974; vol. 1 Gottlieb, Shu (br000035) 1997; 39 Gottlieb, Shu, Solomonoi, Vandeven (br000040) 1992; 43 Shizgal, Jung (br000045) 2003; 161 Martínez, De Pierro (br000080) 2010; 234 Allouche, Cuyt (br000070) 1994; 5 Canuto, Hussaini, Quarteroni, Zang (br000030) 1988 Kantorovich, Krylov (br000050) 1958 Allouche (10.1016/j.cam.2011.11.027_br000070) 1994; 5 Martínez (10.1016/j.cam.2011.11.027_br000080) 2010; 234 Gelb (10.1016/j.cam.2011.11.027_br000010) 2008; 36 Eckhoff (10.1016/j.cam.2011.11.027_br000015) 1995; 64 Rutishauser (10.1016/j.cam.2011.11.027_br000065) 1957 Shizgal (10.1016/j.cam.2011.11.027_br000045) 2003; 161 Henrici (10.1016/j.cam.2011.11.027_br000060) 1974; vol. 1 Archibald (10.1016/j.cam.2011.11.027_br000085) 2008; 58 Lanczos (10.1016/j.cam.2011.11.027_br000025) 1996 Kantorovich (10.1016/j.cam.2011.11.027_br000050) 1958 Gottlieb (10.1016/j.cam.2011.11.027_br000040) 1992; 43 Krylov (10.1016/j.cam.2011.11.027_br000090) 2007; 18 Gragg (10.1016/j.cam.2011.11.027_br000055) 1972; 14 Beckermann (10.1016/j.cam.2011.11.027_br000075) 1996; 12 Gottlieb (10.1016/j.cam.2011.11.027_br000035) 1997; 39 Canuto (10.1016/j.cam.2011.11.027_br000030) 1988 Gelb (10.1016/j.cam.2011.11.027_br000005) 2000; 38 Eckhoff (10.1016/j.cam.2011.11.027_br000020) 1995; 64 |
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| Title | Detecting discontinuity points from spectral data with the quotient-difference (qd) algorithm |
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