Robust Processing of Nonstationary Signals

Techniques for processing signals corrupted by non-Gaussian noise are referred to as the robust techniques. They have been established and used in science in the past 40 years. The principles of robust statistics have found fruitful applications in numerous signal-processing disciplines especially in digital image processing and signal processing for communications. Median, myriad, meridian, L filters (with their modifications), and signal-adaptive realizations form a powerful toolbox for diverse applications. All of these filters have low-pass characteristic. This characteristic limits their application in analysis of diverse nonstationary signals where impulse, heavy-tailed, or other forms of the non-Gaussian noise can appear: FM, radar and speech signal processing, and so forth. Recent research activities and studies have shown that combination of nonstationary signals and non-Gaussian noise can be observed in some novel emerging applications such as internet traffic monitoring and digital video coding. Several techniques have been recently proposed for handling signal filtering, parametric/nonparametric estimation, and feature extraction, of nonstationary and signals with high-frequency content corrupted by non-Gaussian noise. One approach is based on filtering in time domain. Here, the standard median/myriad forms are modified in such a manner to allow negative and complex-valued weights. This group of techniques is able to produce all filtering characteristics: high-pass, stop-band, and band-pass. As an alternative, the robust filtering techniques are proposed in spectral (frequency-Fourier, DCT, wavelet, or in the time-frequency) domain. The idea is to determine robust transforms having ability to eliminate or surpass influence of non-Gaussian noise. Then, filtering, parameter estimation, and/or feature extraction is performed using the standard means. Other alternatives are based on the standard approaches (optimization, iterative, and ML strategies) modified for nonstationary signals or signals with high-frequency content. Since these techniques are increasingly popular, the goal of this special issue is to review and compare them, propose new techniques, study novel application fields, and to consider their implementations. In this special issue, we have been able to select 11 papers on a variety of related topics. The first three papers are related to processing of FM signals in the spectral and the time-frequency domains. The main tool is the robust DFT that can be used for development of various robust tools in the spectral domain. The paper " An overview of the adaptive robust DFT " (A. Roenko et al.) presents an overview of the basic principles and applications of the robust-DFT approach, which is used for robust processing of …