TY - GEN
T1 - Adaptive signal and system approximation and strong divergence
AU - Boche, Holger
AU - Monich, Ullrich J.
N1 - Publisher Copyright:
© 2015 IEEE.
PY - 2015/8/4
Y1 - 2015/8/4
N2 - Many divergence results for sampling series are in terms of the limit superior and not the limit. This leaves the possibility of a convergent subsequence. If there exists a convergent subsequence, adaptive signal processing techniques can be used. In this paper we study sampling-based signal reconstruction and system approximation processes for the space PWπ1 of bandlimited signals with absolutely integrable Fourier transform. For all analyzed examples, which include the peak value of the Shannon and the conjugated Shannon sampling series, we prove strong divergence, i.e., divergence for all subsequences. Hence, adaptive signal processing techniques do not help in these cases. We further analyze whether an adaptive choice of the reconstruction functions in the oversampling case can improve the behavior.
AB - Many divergence results for sampling series are in terms of the limit superior and not the limit. This leaves the possibility of a convergent subsequence. If there exists a convergent subsequence, adaptive signal processing techniques can be used. In this paper we study sampling-based signal reconstruction and system approximation processes for the space PWπ1 of bandlimited signals with absolutely integrable Fourier transform. For all analyzed examples, which include the peak value of the Shannon and the conjugated Shannon sampling series, we prove strong divergence, i.e., divergence for all subsequences. Hence, adaptive signal processing techniques do not help in these cases. We further analyze whether an adaptive choice of the reconstruction functions in the oversampling case can improve the behavior.
KW - Hilbert transform
KW - Paley-Wiener space
KW - linear time-invariant system
KW - reconstruction
KW - strong divergence
UR - http://www.scopus.com/inward/record.url?scp=84946047519&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2015.7178645
DO - 10.1109/ICASSP.2015.7178645
M3 - Conference contribution
AN - SCOPUS:84946047519
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 3616
EP - 3620
BT - 2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015
Y2 - 19 April 2014 through 24 April 2014
ER -