Frequency analysis of noisy short-time stationary signals using filter-diagonalization

Spectral reconstruction of short signals is a problem relevant to many areas of engineering and science. Classical techniques, e.g. Fourier transform (FT) and the wavelet transform (WT) fail to provide accurate estimates of the low frequency content of the signal due to the inherent limitations formulated by the Heisenberg uncertainty principle. To cope with the problem this paper brings up the method of filter-diagonalization (FD), developed in the physical chemistry community and successfully applied in the noise-free context. A natural question occurs as to whether it is robust to noise contaminating the signal and thus applicable to signal processing problems. In this paper the FD method is first re-derived from the point of view of linear state-space systems dynamics. It is shown that the original FD modifies to an essentially stochastic generalized eigenvalue problem with underlying matrices being normally distributed. The results of a Monte Carlo simulation study are summarized showing that the FD method displays monotonous behaviour with respect to the noise and the design parameters. Most importantly, the method turns out to be robust to noise, i.e., it can provide accurate spectral estimates for noise-to-signal ratios as high as 50%.