Accuracy of spike-train Fourier reconstruction for colliding nodes

Andrey Akinshin; Dmitry Batenkov; Yosef Yomdin

Accuracy of spike-train Fourier reconstruction for colliding nodes

Andrey Akinshin, Dmitry Batenkov, Yosef Yomdin

Department of Mathematics

Weizmann Institute of Science

Research output: Contribution to journal › Conference article › peer-review

Abstract

We consider a signal reconstruction problem for signals F of the form F(x) = Sigma(d)(j=1) a(j)delta (x - x(j)) from their Fourier transform F(F)(s) = integral(infinity)(-infinity) F(x)e(-isx) dx. We assume F(F)(s) to be known for each s is an element of [-N, N] with an absolute error not exceeding epsilon > 0. We give an absolute lower bound (which is valid with any reconstruction method) for the "worst case" reconstruction error of F from.F(F) for situations where the x(j) nodes are known to form an 1 elements cluster contained in an interval of length h

Original language	English
Pages (from-to)	617-621
Number of pages	5
Journal	2015 INTERNATIONAL CONFERENCE ON SAMPLING THEORY AND APPLICATIONS (SAMPTA)
State	Published - 2015
Event	International Conference on Sampling Theory and Applications (SampTA) - Washington, United States Duration: 25 May 2015 → 29 May 2015 Conference number: 2015

Access to Document

https://arxiv.org/abs/1502.06932License: Other

Cite this

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title = "Accuracy of spike-train Fourier reconstruction for colliding nodes",

abstract = "We consider a signal reconstruction problem for signals F of the form F(x) = Sigma(d)(j=1) a(j)delta (x - x(j)) from their Fourier transform F(F)(s) = integral(infinity)(-infinity) F(x)e(-isx) dx. We assume F(F)(s) to be known for each s is an element of [-N, N] with an absolute error not exceeding epsilon > 0. We give an absolute lower bound (which is valid with any reconstruction method) for the {"}worst case{"} reconstruction error of F from.F(F) for situations where the x(j) nodes are known to form an 1 elements cluster contained in an interval of length h",

author = "Andrey Akinshin and Dmitry Batenkov and Yosef Yomdin",

year = "2015",

language = "الإنجليزيّة",

pages = "617--621",

note = "International Conference on Sampling Theory and Applications (SampTA) ; Conference date: 25-05-2015 Through 29-05-2015",

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TY - JOUR

T1 - Accuracy of spike-train Fourier reconstruction for colliding nodes

AU - Akinshin, Andrey

AU - Batenkov, Dmitry

AU - Yomdin, Yosef

N1 - Conference code: 2015

PY - 2015

Y1 - 2015

N2 - We consider a signal reconstruction problem for signals F of the form F(x) = Sigma(d)(j=1) a(j)delta (x - x(j)) from their Fourier transform F(F)(s) = integral(infinity)(-infinity) F(x)e(-isx) dx. We assume F(F)(s) to be known for each s is an element of [-N, N] with an absolute error not exceeding epsilon > 0. We give an absolute lower bound (which is valid with any reconstruction method) for the "worst case" reconstruction error of F from.F(F) for situations where the x(j) nodes are known to form an 1 elements cluster contained in an interval of length h

AB - We consider a signal reconstruction problem for signals F of the form F(x) = Sigma(d)(j=1) a(j)delta (x - x(j)) from their Fourier transform F(F)(s) = integral(infinity)(-infinity) F(x)e(-isx) dx. We assume F(F)(s) to be known for each s is an element of [-N, N] with an absolute error not exceeding epsilon > 0. We give an absolute lower bound (which is valid with any reconstruction method) for the "worst case" reconstruction error of F from.F(F) for situations where the x(j) nodes are known to form an 1 elements cluster contained in an interval of length h

M3 - مقالة من مؤنمر

SP - 617

EP - 621

JO - 2015 INTERNATIONAL CONFERENCE ON SAMPLING THEORY AND APPLICATIONS (SAMPTA)

JF - 2015 INTERNATIONAL CONFERENCE ON SAMPLING THEORY AND APPLICATIONS (SAMPTA)

T2 - International Conference on Sampling Theory and Applications (SampTA)

Y2 - 25 May 2015 through 29 May 2015

ER -