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Computing Hilbert Transform and Spectral Factorization for Signal Spaces of Smooth Functions

Abstract: 

Although the Hilbert transform and the spectral factorization are of central importance in signal processing,
both operations can generally not be calculated in closed form. Therefore, algorithmic solutions are prevalent which provide an approximation of the true solution. Then it is important to effectively control the approximation error of these approximate solutions. This paper characterizes for both operations precisely those signal spaces of differentiable functions for which such an effective control of the approximation error is possible. In other words, the paper provides a precise characterization of signal spaces of smooth functions on which these two operations are computable on Turing machines.

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Paper Details

Authors:
Submitted On:
14 May 2020 - 12:03pm
Short Link:
Type:
Presentation Slides
Event:
Presenter's Name:
Volker Pohl
Paper Code:
SPTM-L1.2
Document Year:
2020
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Document Files

BoPo_ICASSP2605.pdf

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[1] , "Computing Hilbert Transform and Spectral Factorization for Signal Spaces of Smooth Functions", IEEE SigPort, 2020. [Online]. Available: http://sigport.org/5314. Accessed: Sep. 26, 2020.
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url = {http://sigport.org/5314},
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publisher = {IEEE SigPort},
title = {Computing Hilbert Transform and Spectral Factorization for Signal Spaces of Smooth Functions},
year = {2020} }
TY - EJOUR
T1 - Computing Hilbert Transform and Spectral Factorization for Signal Spaces of Smooth Functions
AU -
PY - 2020
PB - IEEE SigPort
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. (2020). Computing Hilbert Transform and Spectral Factorization for Signal Spaces of Smooth Functions. IEEE SigPort. http://sigport.org/5314
, 2020. Computing Hilbert Transform and Spectral Factorization for Signal Spaces of Smooth Functions. Available at: http://sigport.org/5314.
. (2020). "Computing Hilbert Transform and Spectral Factorization for Signal Spaces of Smooth Functions." Web.
1. . Computing Hilbert Transform and Spectral Factorization for Signal Spaces of Smooth Functions [Internet]. IEEE SigPort; 2020. Available from : http://sigport.org/5314