Robust L-estimation based forms of signal transforms and time-frequency representations

The L-estimation based signal transforms and time-frequency (TF) representations are introduced by considering the corresponding minimization problems in the Huber (1981, 1998) estimation theory. The standard signal transforms follow as the maximum likelihood solutions for the Gaussian additive noise environment. For signals corrupted by an impulse noise, the median-based transforms produce robust estimates of the non-noisy signal transforms. When the input noise is a mixture of Gaussian and impulse noise, the L-estimation-based signal transforms can outperform other estimates. In quadratic and higher order TF analysis, the resulting noise is inherently a mixture of the Gaussian input noise and an impulse noise component. In this case, the L-estimation-based signal representations can produce the best results. These transforms and TF representations give the standard and the median-based forms as special cases. A procedure for parameter selection in the L-estimation is proposed. The theory is illustrated and checked numerically.