EXTRACTION OF SPECTRAL INFORMATION FROM A SHORT-TIME SIGNAL USING FILTER-DIAGONALIZATION - RECENT DEVELOPMENTS AND APPLICATIONS TO SEMICLASSICAL REACTION DYNAMICS AND NUCLEAR-MAGNETIC-RESONANCE SIGNALS

Filter-diagonalization [M. R. Wall and D. Neuhauser, J. Chem. Phys. 10 2, 8011 (1995)] is a new method for extracting frequencies and damping constants from a short-time segment of any time-dependent signal, whe ther of quantum origin or not. The method is efficient and able to han dle signals with, e.g., millions of (possibly overlapping) frequencies , since it concentrates on specific spectral ranges. The method was sh own to be a powerful tool for extracting eigenstates and normal-modes, and for reducing propagation times, in several recent works by us, by Mandelshtam and Taylor (who recently introduced the box filter) and b y other groups. Here we extend the method in several directions: first , we show how it can be used with a filter of any farm. Next, we show how the methodology may be extended to treat multi-dimensional signals , of the type that appears, e.g., in 2-D nuclear magnetic resonance (N MR). Finally, we exemplify the performance of the various filters for two types of signals where the time-reduction property is potentially quite important: 1D NMR and a correlation function from a semiclassica l propagation (due to Grossmann) analyzed recently with a box filter. Significant reduction in required signal lengths, compared with direct Fourier transform, are found in both cases. (C) 1998 American Institu te of Physics. [S0021-9606(98)01220-3]