Robust time-frequency analysis: Definitions and realizations

In signal analysis the standard linear signal transforms follow as the maximum likelihood solutions for the Gaussian additive noise environment. In some applications signals are corrupted by a heavy-tailed kind of noise. The resulting noise in quadratic and higher order time-frequency distributions (TFD) is inherently a mixture of the Gaussian input noise and an impulse noise component, due to the higher order functions of a signal. For these forms of input or resulting noise the robust signal transforms and TFDs can outperform standard ones. Several forms of the robust TFDs are considered: iterative based, median based, and L-estimation based representations. In addition to the overview of these recently introduced forms, in this paper we propose a recursive on-line realization of the robust TFDs based on the robust STFT. It is shown that higher order TFDs, developed by using the robust STFT in the initial stage, and calculated in recursive manner, produce significantly better results than their counterparts based on the local autocorrelation function.