Timeline for What is the importance of convergence of variation of Fourier reconstruction to that of variation of the function?
Current License: CC BY-SA 4.0
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| Feb 8, 2019 at 7:04 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Jul 24, 2015 at 13:31 | history | bounty ended | CommunityBot | ||
| Jul 22, 2015 at 12:02 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jul 22, 2015 at 10:49 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jul 22, 2015 at 10:14 | comment | added | Rajesh D | Basically I dont want any conditions on $f$ like knowledge of jumps. | |
| Jul 22, 2015 at 10:12 | comment | added | Rajesh D | Here in OP, Fourier reconstruction does not confine to using only finite Fourier coefficients but using all coefficients in the form of $N\to\infty$, asking for an asymptotic result, just like convergnce of Fourier series. Fourier series itself is one type of Fourier reconstruction. | |
| Jul 22, 2015 at 10:08 | comment | added | Rajesh D | You got the question almost right, but my the intention was not for any particular application, it is asking for a theoretical result and not tied to any application. I must say your answer is useful in many ways, but the intention of the question is to find a theoretical result for any function without laying out any physical or application oriented constraints like knowledge of jumps, etc. | |
| Jul 22, 2015 at 7:56 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jul 22, 2015 at 7:56 | comment | added | Carlo Beenakker | Wouldn't that depend on the type of application? In the particular application (to segmented MRI scans) I mention above the jumps are at known locations. I actually thought the question of the OP was about Fourier reconstruction methods in general, not tied to some particular application. Have I misunderstood the question? | |
| Jul 22, 2015 at 4:26 | comment | added | Rajesh D | "The requirement for an exponentially accurate solution is that the location of the jump discontinuity is known in advance", Nothing is known in advance! One can never get the exact location of jump from finite Fourier coefficients. | |
| Jul 17, 2015 at 11:37 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jul 16, 2015 at 13:36 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jul 16, 2015 at 13:28 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jul 16, 2015 at 12:52 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Jul 16, 2015 at 12:46 | history | answered | Carlo Beenakker | CC BY-SA 3.0 |