Deterministic exponential modeling techniques for high spectral resolution time-frequency distributions

A new class of time-frequency distribution kernels is introduced. Kernels in this class map the sinusoidal components in the data to auto-terms of undamped sinusoids and cross-terms of damped sinusoids in the local autocorrelation function (LAF). This property allows deterministic exponential modeling of the LAF for improved spectral resolution. Using the backward linear prediction approach, the roots of the polynomial corresponding to the auto-terms and cross-terms are discriminated by their location whether they are on or outside the unit circle. An analysis of the noise in the LAF is also presented. It is shown that the cross-correlation between any two terms in the LAF is zero. It is also shown that the autocorrelation function of the terms produced by the interaction of the signal and the noise components in the data has the same form as the noise-free LAF, but with a different kernel. These terms are primarily responsible for the frequency bias at low SNR, and their effect can only be removed by imposing a new set of constraints on the original time-frequency kernel.<>