Robust signal analysis based on the L-statistic was introduced for signals disturbed with high additive impulse noise.
The basic idea is that a certain, usually large number of arbitrary positioned signal samples is declared as heavily
corrupted by noise. Then, these samples are removed. Thus, they can be considered as absent or unavailable. Hence, the
L-statistics significantly reduces the number of available signal samples. Moreover these samples are randomly
distributed, so an efficient analysis of such signals invokes the compressive sensing reconstruction algorithms. Also, it
will be shown that the variance of noise, produced by missing samples, can be used as powerful tool for signal
reconstruction. Additionally, in order to provide separation of stationary and nonstationary signals the L-statistic is
combined with compressive sensing algorithms. The theoretical considerations are verified by various examples, where
discrete forms of the Fourier transform and short-time Fourier transform are used to demonstrate the effective integration
of the two techniques.