Multiscale filter diagonalization method for spectral analysis of noisy data with nonlocalized features

被引:25
作者
Chen, JH [1 ]
Mandelshtam, VA [1 ]
机构
[1] Univ Calif Irvine, Dept Chem, Irvine, CA 92697 USA
关键词
D O I
10.1063/1.481005
中图分类号
O64 [物理化学(理论化学)、化学物理学];
学科分类号
070304 ; 081704 ;
摘要
Stability and performance of the filter diagonalization method (FDM) for harmonic inversion [i.e., fitting a time signal by C(t) = Sigma(k) d(k)e(-it omega k)] of noisy data are examined. Although FDM is capable to extract accurately the parameters of narrow spectral peaks, in the presence of broad peaks (or strong background spectrum) and noise, the FDM ersatz spectrum, i.e., I(omega) = Sigma(k)d(k)/(omega(k)-omega), maybe distorted in some regions and be sensitive to the FDM parameters, such as window size, window position, etc. Some simple hybrid methods, that can correct the ersatz spectrum, are discussed. However, a more consistent approach, the multiscale FDM, is introduced to solve the instability problem, in which some coarse basis vectors describing (in low resolution) the global behavior of the spectrum are added to the narrow band Fourier basis. The multiscale FDM is both stable and accurate, even when the total size of the basis (i.e., the number of coarse plus narrow band basis vectors) used is much smaller than what would previously be considered as necessary for FDM. This, in turn, significantly reduces the computation cost. Extension of the 1D multiscale FDM to a multidimensional case is also presented. (C) 2000 American Institute of Physics. [S0021-9606(00)01910-3].
引用
收藏
页码:4429 / 4437
页数:9
相关论文
共 17 条
[1]   RETRIEVAL OF FREQUENCIES, AMPLITUDES, DAMPING FACTORS, AND PHASES FROM TIME-DOMAIN SIGNALS USING A LINEAR LEAST-SQUARES PROCEDURE [J].
BARKHUIJSEN, H ;
DEBEER, R ;
BOVEE, WMMJ ;
VANORMONDT, D .
JOURNAL OF MAGNETIC RESONANCE, 1985, 61 (03) :465-481
[2]   SPECTRAL ESTIMATION OF COMPLEX TIME-DOMAIN NMR SIGNALS BY LINEAR PREDICTION [J].
GESMAR, H ;
LED, JJ .
JOURNAL OF MAGNETIC RESONANCE, 1988, 76 (01) :183-192
[3]   Reference deconvolution, phase correction, and line listing of NMR spectra by the 1D filter diagonalization method [J].
Hu, HT ;
Van, QN ;
Mandelshtam, VA ;
Shaka, AJ .
JOURNAL OF MAGNETIC RESONANCE, 1998, 134 (01) :76-87
[4]   Harmonic inversion of time cross-correlation functions: The optimal way to perform quantum or semiclassical dynamics calculations [J].
Mandelshtam, VA .
JOURNAL OF CHEMICAL PHYSICS, 1998, 108 (24) :9999-10007
[5]  
Mandelshtam VA, 1998, MAGN RESON CHEM, V36, pS17, DOI 10.1002/(SICI)1097-458X(199806)36:13<S17::AID-OMR287>3.0.CO
[6]  
2-2
[7]   Obtaining proton chemical shifts and multiplets from several 1D NMR signals [J].
Mandelshtam, VA ;
Van, QN ;
Shaka, AJ .
JOURNAL OF THE AMERICAN CHEMICAL SOCIETY, 1998, 120 (46) :12161-12162
[8]   Harmonic inversion of time signals and its applications [J].
Mandelshtam, VA ;
Taylor, HS .
JOURNAL OF CHEMICAL PHYSICS, 1997, 107 (17) :6756-6769
[9]   Application of the filter diagonalization method to one- and two-dimensional NMR spectra [J].
Mandelshtam, VA ;
Taylor, HS ;
Shaka, AJ .
JOURNAL OF MAGNETIC RESONANCE, 1998, 133 (02) :304-312
[10]   Multidimensional harmonic inversion by filter-diagonalization [J].
Mandelshtam, VA ;
Taylor, HS .
JOURNAL OF CHEMICAL PHYSICS, 1998, 108 (24) :9970-9977