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On the Computability of System Approximations under Causality Constraints

Abstract: 

Approximating the transfer function of stable causal linear systems by a basis expansion is a common task in signal- and system theory. This paper characterizes a scale of signal spaces, containing stable causal transfer functions, with a very simple basis (the Fourier basis) but which is not computable. Thus it is not possible to determine the coefficients of this basis expansion on any digital computer such that the approximation converges to the desired function.
Since the Fourier basis is not computable, the second part of the paper investigates whether there exist better bases.
To this end, the notion of a computational basis is introduced and it is shown that there exists no computational basis in these spaces. The paper characterizes also subspaces on which computational bases do exist.

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Paper Details

Authors:
Holger Boche, Volker Pohl
Submitted On:
13 April 2018 - 6:04am
Short Link:
Type:
Poster
Event:
Presenter's Name:
Volker Pohl
Paper Code:
SPTM-P10.4
Document Year:
2018
Cite

Document Files

BochePohl_ICASSP18.pdf

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[1] Holger Boche, Volker Pohl, "On the Computability of System Approximations under Causality Constraints", IEEE SigPort, 2018. [Online]. Available: http://sigport.org/2677. Accessed: Oct. 24, 2020.
@article{2677-18,
url = {http://sigport.org/2677},
author = {Holger Boche; Volker Pohl },
publisher = {IEEE SigPort},
title = {On the Computability of System Approximations under Causality Constraints},
year = {2018} }
TY - EJOUR
T1 - On the Computability of System Approximations under Causality Constraints
AU - Holger Boche; Volker Pohl
PY - 2018
PB - IEEE SigPort
UR - http://sigport.org/2677
ER -
Holger Boche, Volker Pohl. (2018). On the Computability of System Approximations under Causality Constraints. IEEE SigPort. http://sigport.org/2677
Holger Boche, Volker Pohl, 2018. On the Computability of System Approximations under Causality Constraints. Available at: http://sigport.org/2677.
Holger Boche, Volker Pohl. (2018). "On the Computability of System Approximations under Causality Constraints." Web.
1. Holger Boche, Volker Pohl. On the Computability of System Approximations under Causality Constraints [Internet]. IEEE SigPort; 2018. Available from : http://sigport.org/2677