Three novel high-resolution nonlinear methods for fast signal processing

Three novel nonlinear parameter estimators are devised and implemented for accurate and fast processing of experimentally measured or theoretically ge nerated time signals of arbitrary length. The new techniques can also be us ed as powerful tools for diagonalization of large matrices that are customa rily encountered in quantum chemistry and elsewhere. The key to the success and the common denominator of the proposed methods is a considerably reduc ed dimensionality of the original data matrix. This is achieved in a prepro cessing stage called beamspace windowing or band-limited decimation. The me thods are decimated signal diagonalization (DSD), decimated linear predicto r (DLP), and decimated Pade approximant (DPA). Their mutual equivalence is shown for the signals that are modeled by a linear combination of time-depe ndent damped exponentials with stationary amplitudes. The ability to obtain all the peak parameters first and construct the required spectra afterward s enables the present methods to phase correct the absorption mode. Additio nally, 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 exhibi t an enhanced resolution power relative to the standard fast Fourier transf orm. Of the three methods, DPA is found to be the most efficient computatio nally. (C) 2000 American Institute of Physics. [S0021-9606(00)00440-2].