Two-dimensional filter-diagonalization: spectral inversion of 2D NMR time-correlation signals including degeneracies

Several years ago we introduced a new approach for signal extraction, Filter-Diagonalization, which is capable of handling signals containing millions of points or more. The method was recently extended to handle multidimensional signals, as appear in NMR, by us and separately by Mandelshtam and Taylor. We further extend the original formulation by showing that the method is capable of handling degenerate eigenvalues and eigenstates through the use of a simultaneous diagonalization algorithm. We apply the method to simple two-dimensional NMR signals. Comparisons to a standard FFT treatment show that FDG recovers the salient spectral features using a quarter of the signal required by FFT.