TY - JOUR
T1 - On semi-classical questions related to signal analysis
AU - Helffer, Bernard
AU - Laleg-Kirati, Taous-Meriem
N1 - KAUST Repository Item: Exported on 2020-10-01
PY - 2011/12/1
Y1 - 2011/12/1
N2 - This study explores the reconstruction of a signal using spectral quantities associated with some self-adjoint realization of an h-dependent Schrödinger operator -h2(d2/dx2)-y(x), h>0, when the parameter h tends to 0. Theoretical results in semi-classical analysis are proved. Some numerical results are also presented. We first consider as a toy model the sech2 function. Then we study a real signal given by arterial blood pressure measurements. This approach seems to be very promising in signal analysis. Indeed it provides new spectral quantities that can give relevant information on some signals as it is the case for arterial blood pressure signal. © 2011 - IOS Press and the authors. All rights reserved.
AB - This study explores the reconstruction of a signal using spectral quantities associated with some self-adjoint realization of an h-dependent Schrödinger operator -h2(d2/dx2)-y(x), h>0, when the parameter h tends to 0. Theoretical results in semi-classical analysis are proved. Some numerical results are also presented. We first consider as a toy model the sech2 function. Then we study a real signal given by arterial blood pressure measurements. This approach seems to be very promising in signal analysis. Indeed it provides new spectral quantities that can give relevant information on some signals as it is the case for arterial blood pressure signal. © 2011 - IOS Press and the authors. All rights reserved.
UR - http://hdl.handle.net/10754/561951
UR - http://arxiv.org/abs/arXiv:1009.5372v2
UR - http://www.scopus.com/inward/record.url?scp=84872313377&partnerID=8YFLogxK
U2 - 10.3233/ASY-2011-1054
DO - 10.3233/ASY-2011-1054
M3 - Article
SN - 0921-7134
VL - 75
SP - 125
EP - 144
JO - Asymptotic Analysis
JF - Asymptotic Analysis
IS - 3-4
ER -