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

Stability and performance of the filter diagonalization method (FDM) for ha rmonic 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 ac curately 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 regi ons and be sensitive to the FDM parameters, such as window size, window pos ition, etc. Some simple hybrid methods, that can correct the ersatz spectru m, 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 stab le 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 woul d previously be considered as necessary for FDM. This, in turn, significant ly reduces the computation cost. Extension of the 1D multiscale FDM to a mu ltidimensional case is also presented. (C) 2000 American Institute of Physi cs. [S0021-9606(00)01910-3].