Three novel nonlinear parameter estimators are devised and implemented for accurate and fast processing of experimentally measured or theoretically generated time signals of arbitrary length. The new techniques can also be used as powerful tools for diagonalization of large matrices that are customarily encountered in quantum chemistry and elsewhere. The key to the success and the common denominator of the proposed methods is a considerably reduced dimensionality of the original data matrix. This is achieved in a preprocessing stage called beamspace windowing or band-limited decimation. The methods are decimated signal diagonalization (DSD), decimated linear predictor (DLP), and decimated Padé approximant (DPA). Their mutual equivalence is shown for the signals that are modeled by a linear combination of time-dependent damped exponentials with stationary amplitudes. The ability to obtain all the peak parameters first and construct the required spectra afterwards enables the present methods to phase correct the absorption mode. Additionally, a new noise reduction technique, based upon the stabilization method from resonance scattering theory, is proposed. The results obtained using both synthesized and experimental time signals show that DSD/DLP/DPA exhibit an enhanced resolution power relative to the standard fast Fourier transform. Of the three methods, DPA is found to be the most efficient computationally.
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22 October 2000
Research Article|
October 22 2000
Three novel high-resolution nonlinear methods for fast signal processing
Dž. Belkić;
Dž. Belkić
Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482
Department of Medical Radiation Physics, Karolinska Institute, P.O. Box 260, S-17176 Stockholm, Sweden
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P. A. Dando;
P. A. Dando
Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482
Department of Medical Radiation Physics, Karolinska Institute, P.O. Box 260, S-17176 Stockholm, Sweden
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J. Main;
J. Main
Institut für Theoretische Physik und Synergetik, Universität Stuttgart, D-70550 Stuttgart, Germany
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H. S. Taylor
H. S. Taylor
Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482
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J. Chem. Phys. 113, 6542–6556 (2000)
Article history
Received:
June 06 2000
Accepted:
July 26 2000
Citation
Dž. Belkić, P. A. Dando, J. Main, H. S. Taylor; Three novel high-resolution nonlinear methods for fast signal processing. J. Chem. Phys. 22 October 2000; 113 (16): 6542–6556. https://doi.org/10.1063/1.1310612
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