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Measurement campaigns show the presence of heavy tailed distributions and outliers in key engineering applications, such as radar, biomedicine, communication, speech and image processing, among others. Robust statistical signal processing provides powerful tool to deal with such situations. The complexity of today’s problems and the high robustness requirements impose their own challenges and have triggered new areas of research. The first ever book on robust signal processing provides fundamentals and recent advances in an accessible and motivating manner. It includes advanced robust methods for complex-valued data, robust covariance estimation, penalized regression models, dependent data, robust bootstrap and tensors. Real world examples are used throughout the book to demonstrate the relevance and motivate and illustrate robustness issues. The key algorithms are included in a Matlab Robust Signal Processing Toolbox. In this way, the methods in the book can be easily applied and extended.