An optimal L-estimate form of the Hermite transform for mixture of Gaussian and impulse noise

The paper proposes the optimal robust form of the Hermite transform suitable for analysis of the signals corrupted by a mixture of the impulse and Gaussian noise. The L-estimate form of the Hermite transform is used for reduction of the impulse noise, considering discarded samples as missing ones in the subsequent procedure. The rest of the signal samples are corrupted with Gaussian noise, which is averaged as a part of the L-estimation procedure. The Hermite transform is observed since it is suitable for the analysis of signals in various applications, starting from biomedical (QRS complexes) to communications (UWB signals). The L-estimation approach of the Hermite transform is combined with the distribution that provides minimal bound variance according to the Cramer-Rao bound theory. The theory is verified experimentally on Hermite-like signals.